AN INTRODUCTION TO REASONING EXERCISE BOOK

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					AN INTRODUCTION
 TO REASONING
       —
 EXERCISE BOOK
                          AN INTRODUCTION
                           TO REASONING
                                 —
                           EXERCISE BOOK




                             CATHAL WOODS




                                   2011, 2010

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                                                                                      Ex—1

An Introduction To Reasoning
Exercise Set (1) on Reasoning, Flag Words (2.1-3)

For each passage, (i) say whether the "speaker" is arguing, explaining, or neither
(underline the appropriate choice). (ii) Explain your choice in writing. (If "Neither", state
what the speaker is doing with the words.) If "Arguing" or "Explaining", (iii) underline
the explainee or conclusion and (iv) put any flag words in (parentheses).

Sample:
   A student is speaking to her instructor: (Because) my dog ate my homework, I should
   be allowed to do it again.

   Arguing                  Explaining                   Neither

   An argument because the student is presenting new information to the instructor, who does
   not already believe the conclusion.

(1) Jack is reading a popular science magazine. It reads: Recent research has shown that
    people who rate themselves as "very happy" are less successful financially than
    those who rate themselves as "moderately happy". He says, "Huh! It seems that a
    little unhappiness is good in life."

   Arguing                  Explaining                   Neither




(2) An anthropologist is speaking. People get nicknames based on some distinctive feature
    they possess. And so, Mark, for example, who is 6' 6" is (ironically) called "Smalls",
    while Matt, who looks young, is called "Baby Face". John looks just like his dad, and
    is called "Chip".

   Arguing                  Explaining                   Neither




(3) Henry is lamenting to his friend Bill. I can't stand it any more. I'll tell you why: I'm
    tired of living all alone. No one ever calls me on the phone. And my landlady tried
    to hit me with a mop. (Based on Lou Reed's 'I Can't Stand It', from "Lou Reed".)

   Arguing                  Explaining                   Neither
                                                                                        Ex—2

(4) Two teenaged friends are talking.
      Saida:         I can't go to the show tonight.
      Jordan:        Bummer.
      Saida:         I know! My mother wouldn't let me go out when I asked.


   Arguing                   Explaining                   Neither




(5) A mother is speaking to her teenage son. You should always listen to your mother, and I
    say "no". So, you have to stay in tonight.

   Arguing                   Explaining                   Neither




(6) An economist is speaking. Any time the public receives a tax rebate, consumer
    spending increases. Since the public just received a tax rebate, consumer spending
    will increase.

   Arguing                   Explaining                   Neither




(7) In a letter to the editor. Today's kids are all slackers. American society is doomed.

   Arguing                   Explaining                   Neither




(8) Duke beat Butler 61-59 for the national championship Monday night. Gordon
    Hayward's half-court, 3-point heave for the win barely missed to leave tiny Butler
    one cruel basket short of the Hollywood ending. (Based on an article from Espn.go.com)

   Arguing                   Explaining                   Neither
                                                                                      Ex—3

(9) A detective is speaking: Henry's finger-prints were found on the stolen computer. So, I
    infer that Henry stole the computer.

   Arguing                  Explaining                   Neither




(10) On Monday, Jack is told that his unit ships to Iraq in two days: Well, that sucks. I was
    hoping to go to Henry's birthday party next weekend, but if I'm shipping out on
    Wednesday, I will miss it.

   Arguing                  Explaining                   Neither
                                                                                      Ex—4

An Introduction To Reasoning
Exercise Set (2) on Reasoning, Flag Words (2.1-3)

For each passage, (i) say whether the "speaker" is arguing, explaining, or neither
(underline the appropriate choice). (ii) Explain your choice in writing. (If "Neither", state
what the speaker is doing with the words.) If "Arguing" or "Explaining", (iii) underline
the explainee or conclusion and (iv) put any flag words in (parentheses).

(1) On a political debate program: Hillary Clinton should drop out of the race for
    Democratic Presidential nominee. For every day she stays in the race, McCain gets a
    day free from public scrutiny and the members of the Democratic party get to fight
    one another.

   Arguing                  Explaining                   Neither




(2) You have to be smart to understand the rules of Dungeons and Dragons. Most smart
    people are nerds. So, I bet most people who play D&D are nerds.

   Arguing                  Explaining                   Neither




(3) You already know that God kicked humanity out of Eden before they could eat of
    the tree of life but only after they had eaten of the tree of knowledge of good and
    evil, but you might not know why. It's because Satan wanted to take over God's
    throne and was responsible for their eating from the tree. If humans had eaten of
    both trees they could have been a threat to God.

   Arguing                  Explaining                   Neither




(4) The economy has been in trouble recently. And it's certainly true that cell phone use
    has been rising during that same period. So, I suspect increasing cell phone use is
    bad for the economy.

   Arguing                  Explaining                   Neither
                                                                                      Ex—5

(5) At the market. You know, granola bars generally aren't healthy, even though they say
    "all natural" and things like that. Just check the ingredients: lots of processed sugars.

   Arguing                  Explaining                   Neither




(6) A pet-store salesman is speaking: Strange though it might seem, a small dog makes just
    as effective a guard dog for your home as a big dog. Smaller "yappy" dogs bark
    readily and generate higher-pitched sounds. Most of a dog's effectiveness as a guard
    is due to making a sound, not physical size.

   Arguing                  Explaining                   Neither




(7) An anthropologist is speaking: Different gangs use different colors to distinguish
    themselves. Here are some illustrations: biologists tend to wear some blue, while the
    philosophy gang wears black.

   Arguing                  Explaining                   Neither




(8) A child is thinking out loud. I think my cat must be dead. It isn't in any of its usual
    places, and when I asked my mother if she had seen it, she couldn't look me in the
    eyes.

   Arguing                  Explaining                   Neither




(9) Smith is speaking to his friend, Jones. Since I'm a member of MENSA, I can solve any
    puzzle more quickly than you.

   Arguing                  Explaining                   Neither
                                                                                    Ex—6

(10) In the comments on a biology blog: According to Darwin's theory, my ancestors
    were monkeys. But since that's ridiculous, Darwin's theory is false.

   Arguing                  Explaining                  Neither




(11) If you believe in [the Christian] God and turn out to be incorrect, you have lost
    nothing. But if you don't believe in God and turn out to be incorrect, you will go to
    hell. Believing in God is better in both cases. One should therefore believe in God. (A
    formulation of "Pascal's Wager" by Blaise Pascal.)

   Arguing                  Explaining                  Neither




(12)   Bill and Henry are in Columbus.
       Bill: Good news—I just accepted a job offer in Omaha.
       Henry: That's great. Congratulations! I suppose this means you'll be leaving us,
               then?
       Bill: Yes, I'll need to move sometime before September.

   Arguing                  Explaining                  Neither
                                                                                         Ex—7

An Introduction To Reasoning
Exercise Set (1) on Propositions (2.4)

For each passage, (i) say whether the speaker is arguing or explaining by underlining
either "Arguing" or else "Explaining", (ii) underline the explainee or conclusion, (iii) put
any flag words in (parentheses), (iv) number the propositions and (v) either [bracket]
the reasons as they appear in the passage and note any changes needed due to
propositions being in disguise or containing pronouns, or else write out a numbered list
of complete propositions.

Sample: (1) [Jack's car keys are on the kitchen table.] (2) [There is music coming from
        his room.] (So), (3) Jack is home.

           Arguing                  Explaining

           (2) = There is music coming from Jack's room.

(1) Jack has gone to retrieve a book called Intellectual Virtues from his locker, but is having
    trouble finding it: That book is in here somewhere. I saw it just yesterday.

   Arguing            Explaining




(2) Smith is arguing with Jones: Lookit! The variation in plant species is perfectly
    explained by Darwin's theory. So, it's obvious to anyone with a brain that Darwin's
    theory is true.

   Arguing            Explaining




(3) Jack is at the park, with Jim the Great Dane, in winter. Jim is off his leash. Don't play in
    that yellow snow, Jim! Another dog has peed in it.

   Arguing            Explaining
                                                                                        Ex—8

(4) Gill is forming a resolution: I shouldn't eat anything that comes from something that
    once had a face. The chicken we eat comes from chickens, and chickens have faces.
    Therefore, I won't eat chicken.

   Arguing           Explaining




(5) John McCain, a presidential candidate in the U.S. in 2009, was reportedly not familiar with
    the internet. Lots of folks McCain's age aren't familiar with the internet. After all, he
    is 72. That's why he doesn't know how to get on-line.

   Arguing           Explaining




(6) Henry has just read an article about eating junk food and is wondering whether chocolate is
    healthy. Most people eat chocolate. Human biology has adapted so that we don't
    normally eat things that are dangerous. So, chocolate is not dangerous.

   Arguing           Explaining




(7) Jones, talking to Smith, discusses the talent in N.W.A. Of the members of N.W.A., only a
    few had any real talent. Dr. Dre still makes money in the recording industry, and Ice
    Cube made a nice career out of acting later on. But I bet you can't you think of any
    other member who is still well-known.

   Arguing           Explaining
                                                                                   Ex—9

(8) Jack and Gill are at a restaurant. Consider Jack's reasoning:
    Jack: Young children should not be allowed in restaurants after dinner time.
    Gill: Why is that?
    Jack: Late at night, young children tend to get cranky, and when they get cranky they
           create a fuss, which other people in the restaurant can hear.
    Gill: I agree, but that hardly stops them from eating.
    Jack: Yeah, but it's not just about eating. Many adults who go out to eat at night are
           attempting to have a conversation and the noise of children can ruin that
           conversation.

   Arguing          Explaining
                                                                                    Ex—10

An Introduction To Reasoning
Exercise Set (2) on Propositions (2.4)

For each passage, (i) say whether the speaker is arguing or explaining by underlining
either "Arguing" or else "Explaining", (ii) underline the explainee or conclusion, (iii) put
any flag words in (parentheses), (iv) number the propositions and (v) either [bracket]
the reasons as they appear in the passage and note any changes needed due to
propositions being in disguise or containing pronouns, or else write out a numbered list
of complete propositions.

(1) A policeman tries a rational approach: Underage drinking is immoral. After all, it's
    illegal, and most things that are against the law are immoral.

   Arguing           Explaining




(2) Smith notices that Henry drinks Guinness and never beer. Jones says: Most Irish prefer
    stout over lager. That's why Henry, who is Irish, prefers stout over lager.

   Arguing           Explaining




(3) In a discussion of ethics: Abortion is not always morally wrong. Are you trying to tell
    me that women who are pregnant as a result of rape must keep the child?

   Arguing           Explaining




(4) Smith and Jones discuss the firing of another employee: Smith: Cindy was fired because
    she never shows up on time.

   Arguing           Explaining
                                                                                           Ex—11

(5) Henry is going to take care of Jack's dog Jim while Jack is on holiday. They (three) are out for
    a practice walk. Jack says: You see Jim pulling on the leash like that? That's because he
    chases any squirrel he gets a whiff of and he's probably smelling a squirrel right
    now.

   Arguing             Explaining




(6) Bill responds to a flat-earther: The sky looks different in the northern and southern
    parts of the earth. This would be so if the earth were spherical in shape. Also, we
    have globes, which are modeled on the Earth. So, how can the Earth not be round?

   Arguing             Explaining




(7) Part of a conversation at Championship Records (record store): I'd argue that Anthrax's
    cover of "Bring the Noise" was a nice way to combine rap and rock music. The music
    and the lyrics complemented each other well. The song is noticeably different
    without having to change the basic feel or flow. It was much like Run DMC and
    Aerosmith's work on 'Walk This Way'.

   Arguing             Explaining




(8) An advertisement: The iPhone 3G is a better buy than the iPhone. "3G" means that
    internet access has become faster. The 3G is also equipped with real-time GPS,
    unlike the original iPhone. And at the cheaper price of $200, the 3G is clearly the
    better buy.

   Arguing             Explaining
                                                                                     Ex—12

(9) At a school board meeting: Since creationism can be discussed effectively as a scientific
    model, and since evolutionism is fundamentally a religious philosophy rather than a
    science, it is unsound educational practice for evolution to be taught and promoted
    in the public schools to the exclusion or detriment of special creation. (Kitcher (1982)
    p. 177, citing Morris.)

   Arguing           Explaining
                                                                                     Ex—13

An Introduction To Reasoning
Exercise Set (1) on Standard Forms & Diagrams (3.1-2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. Then, (vi) write (or type or
paste) the argument in standard form and (vii) diagram it. In diagramming the
argument, use the numbers from the standard form rather than writing out a separate
key. In both the standard form and the diagram, use "J" or "E" to denote an argument or
explanation.

Sample:     (1) [Chicago is north of Columbus], and (2) [it is north of Miami]. And, of
           course, (3) [Miami is north of Memphis]. (Therefore), (4) Chicago is north of
           Memphis.

       (1) Chicago is north of Columbus.                      1+2+3
       (2) Columbus is north of Miami.
       (3) Miami is north of Memphis.                           J
     J     -----------------------------------------
       (4) Chicago is north of Memphis.                             4


(1) A proposal at a business: Since outsourcing jobs to foreign countries is often more cost-
    effective than doing them in-house, we [Company C] should look into finding
    foreign companies to take care of our customer service.




(2) A terrible realization: Chips Ahoy cookies aren't healthy food, and neither are Oreo
    cookies. So, I guess Girl Scout Cookies aren't healthy!
                                                                                     Ex—14

(3) The variation in plant species is perfectly explained by Darwin's theory. So,
    Darwin's theory is true.




(4) Listen, we could really use Yo-Yo Ma in the band. You're always saying how you
    want to take our sound in a different direction. He's trained at Julliard, which is a lot
    more than I can say for any of us.




(5) Part of a conversation at Championship Records: How can we explain the remarkable
    fact that people still remember Wheatus' song "Teenage Dirtbag", even though the
    band quickly fell out of the lime-light? In a word: catchiness.
                                                                                     Ex—15

(6) A detective inspects a burgled premises. There are no marks on any of the doors or
    windows. Therefore, the burglar must have had a key to the premises.




(7) A university president speaks: Hingson's report from 2005 found that 1700 (U.S.)
    students died from alcohol-related injuries and another 600,000 more were non-
    fatally injured. Hingson's report is reliable. It follows that many college students
    these days drink too much.




(8) At a school board meeting: Since creationism can be discussed effectively as a scientific
    model, and since evolutionism is fundamentally a religious philosophy rather than a
    science, it is unsound educational practice for evolution to be taught and promoted
    in the public schools to the exclusion or detriment of special creation. (Kitcher (1982)
    p. 177, citing Morris.)
                                                                                   Ex—16

An Introduction To Reasoning
Exercise Set (2) on Standard Forms & Diagrams (3.1-2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. Then, (vi) write (or type or
paste) the argument in standard form and (vii) diagram it. In diagramming the
argument, use the numbers from the standard form rather than writing out a separate
key. In both the standard form and the diagram, use "J" or "E" to denote an argument or
explanation.

(1) In an ad for a soft drink: Aarg cola offers a taste that's crisp and refreshing. It's
    treasured by pirates everywhere. Try one today!




(2) At a medical conference: Studies show that the obese have a greater incidence of blood
    clots. They also show that the obese have a greater incidence of heart attacks. These
    two factors explain the reduced average length of life.




(3) A policeman tries a different approach: Underage drinking is immoral. After all, it's
    illegal, and most things that are against the law are immoral.
                                                                                  Ex—17

(4) A frequent smoker speaks: No research has conclusively shown that cigarettes cause
    lung cancer and emphysema. So, cigarettes are not dangerous.




(5) An employee is speaking to her boss about another worker: Cindy never shows up on
    time. Most employers fire employees who don't show up on time without a good
    reason. So, she should be fired.




(6) A guest at a dinner has refused the lamb: Why am I not eating the lamb? Simple: eating
    anything that has—or had!—a face is too hard for me to bear.
                                                                                   Ex—18

(7) Jack is frustrated with Gill's laziness: I had to do the laundry last week and the week
    before that. Why don't you do it for once, Gill?




(8) Women were not citizens in nineteenth century U.S.A. because a citizen is someone
    who is eligible, under the constitution of the nation, to participate in some form of
    judgment or deliberation.
                                                                                   Ex—19

An Introduction To Reasoning
Exercise Set (1) on Complex Reasoning (3.3-5)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Diagram the
reasoning. Use "J" or "E" to indicate an argument or explanation.

Sample: (1) [Potatoes are vegetables], and (2) [vegetables are good for you]. (So), (3)
     [potatoes are good for you]. (4) [They're also cheap]. (So), (5) you should be sure
     to include them in your diet.

   (4) = Potatoes are cheap.
   (5) = You should include potatoes in your diet.

                                                                       1+2



                                                                        3+4

                                                                         J

                                                                             5



(1) House-builders work awfully hard. Their workday is longer than 8 hours; the job
    involves heavy lifting and there's the possibility of injury. They also have to contend
    with the weather.
                                                                                  Ex—20

(2) Jim will go after anything interesting he gets a whiff of. It looks like he's smelling
    something right now. So, he'll go running after it. We don't want to lose him, so,
    hold on tight.




(3) Deepwater Horizon's poor workmanship and lax safety standards are responsible
    for causing the oil leak in the Gulf. Since those who are responsible should pay for
    the resulting costs, Deepwater Horizon should pay for the costs.
                                                                               Ex—21

(4) Most employers fire employees who don't show up on time without a good reason.
    Cindy never shows up on time. She has no excuse—she lives only two minutes from
    her place of employment. So, she should be fired by her employer.




(5) We don't know for certain that the accused is guilty. The old woman's testimony is
    questionable, since she was 60 feet away and it was night-time, and the man's
    testimony is dodgy, too—how could he have heard the argument with the train
    rolling by? Those are the only witnesses to the crime. (Based on 12 Angry Men)
                                                                                   Ex—22

(6) When people are happy, they don't strive as much as when they are not. This is the
    conclusion of research which found that slightly less happy people are more
    successful than those who are completely content with life. Anti-depressants make
    people feel happy when they otherwise might not. As a result, anti-depressants
    should be used only in extreme situations.




(7) People still remember Wheatus' song "Teenage Dirtbag". This would be explained if
    it has a catchy tune. There's no better explanation—the vocals were bad and the
    lyrics were neither deep nor clever. So, the reason people remember it is because it is
    catchy.
                                                                                      Ex—23

(8) My accuser says I [Socrates] believe in spiritual matters but not in gods. Now, who
    could believe in spiritual matters without believing in spirits? So, I believe in spirits.
    And spirits are the offspring of gods. Since no one can believe in the offspring and
    not believe in the parents, then, of course, I must believe in gods. So, it's clear that
    contradicts himself, and so, that he doesn't know what he's talking about. (Based on
    Plato's Socrates' Defense)
                                                                                  Ex—24

An Introduction To Reasoning
Exercise Set (2) on Complex Reasoning (3.3-5)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Diagram the
reasoning. Use "J" or "E" to indicate an argument or explanation.

(1) Chips Ahoy cookies aren't healthy, and neither are Oreo cookies. So, I guess Girl
    Scout Cookies aren't healthy. I don't want to eat unhealthy food. So, I won't be
    eating any more Girl Scout cookies.




(2) Gas prices are rising sharply due to a shortage in refining capacity and international
    instability. So, the oil companies should increase refining capacity, and the
    government should be active on the world political stage.
                                                                                    Ex—25

(3) We should drastically increase security at our ports. Security is currently extremely
    lax and containers might be used to smuggle in weapons material. What's more,
    human smuggling often goes through ports.




(4) We should close down all of our nuclear plants. Nuclear waste is a terrible
    contaminant, and so if there's an accident it will be terrible. Without nuclear power,
    there will be a shortfall in energy. So, we should invest in alternative energy sources.
                                                                                  Ex—26

(5) We should repress the results of the recent prayer study. Simple-minded people will
    interpret them to mean that there is no God and, without belief in God, will act
    immorally. So, the prayer study will cause simple-minded people to act immorally.
    The immorality of the simple-minded corrupts society. So, society will be corrupted
    by the results of the prayer study. And anything that corrupts society should be
    repressed. So, we should repress the results of the study.




(6) Most employers fire employees who don't show up on time without a good reason.
    Cindy never shows up on time. She has no excuse—she lives only two minutes from
    her place of employment and should be able to get there on time. Cindy also
    normally can't work a full shift because of other obligations. This means that her co-
    workers end up covering her responsibilities. So, she should be fired by her
    employer.
                                                                                    Ex—27

(7) My accuser says I [Socrates] am a complete atheist, but in the indictment, he says
    that I believe in new spiritual matters. Now, who could believe in spiritual matters
    without believing in spirits? So, I believe in spirits. And spirits are the offspring of
    gods. Since no one can believe in the offspring and not believe in the parents, then,
    of course, I must believe in gods. So, he contradicts himself and makes clear that he
    doesn't know what he's talking about. He also says that I willingly corrupt the
    young. But since people corrupted people do bad things to their acquaintances, it
    would be foolish of me to willingly corrupt anyone. So, he contradicts himself and
    again shows that he does not know what he's talking about. (Based on Plato's
    Socrates' Defense)




(8) Apes and chimps are not completely human. And so, research done with them in
    order to gain insights into the human condition is flawed. Flawed research is not
    worth funding. So, psychological research on apes and chimps is not worth funding.
    Another reason not to fund such research is that apes and chimps are sentient
    beings, and so it's not right to do research on them that wouldn't be done on
    humans.
                                                                                     Ex—28

An Introduction To Reasoning
Exercise Set (1) on Objections & Rebuttals (3.6-7)

For each passage, (i) put any flag words in (parentheses), (ii) write out a numbered list
of the propositions in full. (iii) Diagram the passage.

Sample: The estate tax should be abolished once and for all (because) it is immoral—it is
     a second tax on income that already has been taxed. The fact that the budget
     deficit is so great and could be reduced by a return of the tax is irrelevant—if the
     money is ill-gotten, it should not be used for any purpose, reducing the deficit or
     otherwise.

(1) The estate tax should be abolished once and for all.               3
(2) The estate tax is immoral.
(3) The estate tax is a second tax on income that already
        has been taxed.
(4) The budget deficit is the highest ever.                            2         6
(5) The budget deficit could be reduced by a return of
        the [estate] tax.                                          J
(6) If money is ill-gotten, it should not be used for any
        purpose.                                                       1
                                                                           4+5

(1) Jack says that Jim scratches himself because he has fleas. But maybe he has dry skin,
    instead.
                                                                                Ex—29

(2) Republicans argue that Guantanamo must remain open because moving prisoners
    from Guantanamo to main-land U.S.A. puts American citizens at risk. But this is
    absurd. The prisons they would be held in are super-max facilities that are
    completely secure. Indeed, the shoe-bomber and one of the 9/11 plotters are already
    securely incarcerated in U.S. prisons.




(3) Those who argue that Shellie Ross is an unfit mother for "tweeting" during her son's
    drowning simply have their facts wrong. She did not tweet any information until
    she was in the hospital after her son was receiving medical attention.
                                                                                Ex—30

(4) The Associated Press has named Serena Williams as its 'Female Athlete of the Year'
    for 2009, on the basis of winning Wimbledon to add to her two previous grand slam
    wins and her #1 ranking. The AP's decision is a mistake, however. Williams had a
    terrible display of bad behavior in the US Open semi-final. She lost her temper and
    physically threatened a line-judge who had called a foot-foul against her. Athletes
    are role-models to children everywhere and this is not the kind of behavior young
    girls should be imitating.
                                                                                 Ex—31

An Introduction To Reasoning
Exercise Set (2) on Objections & Rebuttals (3.6-7)

For each passage, (i) put any flag words in (parentheses), (ii) write out a numbered list
of the propositions in full. (iii) Diagram the passage.

(1) Chips Ahoy cookies aren't healthy food, and neither are Oreo cookies. So, I guess
    Girl Scout Cookies aren't healthy. I was hoping that they were healthy because
    they're sold by the Girl Scouts, who are generally good people.




(2) The 2000s saw a disputed presidential election, the dot-com bust, 9-11, war in Iraq
    based on mis-interpreted intelligence, hurricane Katrina and a tsunami, and a global
    financial melt-down. For these reasons, USA Today called the decade "grim". But in
    fact, the 2000s were the first decade since the 1900s without a world war, Hitler, or
    the Soviet Union. The decade also saw strong economic growth in China, India,
    Indonesia and Brazil. (via Tyler Cowen, Bryan Caplan. For "grim", see USA Today
    http://blogs.usatoday.com/oped/2009/12/our-opinion-at-the-end-of-grim-decade-
    reasons-for-holiday-cheer.html)
                                                                                  Ex—32

(3) Many undergraduate students in the humanities convince themselves that going to
    grad school is a good idea. They argue that they have an interest in the subject, and
    have received high grades in it. Grad school is also attractive because it offers a
    continuation of a life they're familiar with, in contrast to the uncertainties of the
    working world. They're unaware, however, that their high grades are partly a
    function of grade inflation. More importantly, they fail to realize that the programs
    they are joining do not have their interests at heart, using graduate students
    primarily as cheap teachers. The number of tenured jobs is constantly diminishing
    because of a move to adjunct teaching. Only half of all doctorates work in tenured
    academic positions, there is no choice in where to live, and pay is lower than in jobs
    requiring comparable skills.
                                                                                Ex—33

(4) Those who argue that Shellie Ross is an unfit mother for "tweeting" during her son's
    drowning simply have their facts wrong. She did not tweet any information until
    she was in the hospital and her some was receiving medical attention. She is,
    however, an unfit mother for having sent so many tweets in the time prior to the
    drowning—any parent who spends this much time on Twitter when they have kids
    is obviously not giving them proper attention.
                                                                                     Ex—34

An Introduction To Reasoning
Exercise (1, 2) on Very Long Passages (3.8)

Editorials (and opinion-editorials) provide good opportunities to practice your skills of
argument analysis because they are frequently very messy. Like any argument they
state a claim and offer some justification for it, but the structure of the argument is often
complex—editorials are often joint arguments, and they often consider (and reject)
objections to the opinion.


Read the editorial at
Ex1 http://www.nytimes.com/2007/12/08/opinion/08sat3.html?pagewanted=print
Ex2      http://blogs.usatoday.com/oped/2009/12/debate-on-terror-suspects-our-view-
you-cant-close-gitmo-if-you-dont-move-the-prisoners.html
and follow the following instructions.


         The Article As A Whole
1. What is the overall claim of the article? Is it to support some position? Or to reject
some position?
2. Explain how you know what the overall claim is.


It is often necessary to read the entire piece in order to identify the conclusion, and
indeed, sometimes it is necessary to perform the other steps first. Obvious things to pay
attention to are the title or headline to the piece (though sometimes the title will simply
state the topic, rather than the conclusion), and the opening or closing
sentences/paragraphs, or flag words, or the overall structure of the argument.


         Main Points
3. Summarize the article by writing a single proposition which expresses each main
point.
Do not write out every proposition in the article, unless it is extremely concise. Some
points, however, might only get a single proposition.
You might need to invent a summary proposition that is not in the article itself; if you
do, explain why you have done so.
                                                                                Ex—35

      Diagrams
4. Give a basic diagram involving the summary propositions from step 4.
5. Copy the diagram from step 5 but also add the details.
6. Discuss your diagram at length. Include at a minimum a discussion of the structure of
each part of the diagram, as well as discussing alternate possibilities and explaining
why you chose as you did. If you left out any proposition/point from the article,
explain why.
                                                                                 Ex—36

An Introduction To Reasoning
Exercise Set (1) on Getting Clear on the Meaning (4.2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. Then, (vi) discuss any
issues concerning the meaning of the reasons and target.

Sample
   From the Honey Marketing Board: (1) Eating more honey can help you lower your
   weight! (2) [It increases your metabolism].

   (2) "it" = eating honey

   Both (1) and (2) are somewhat vague. "more" in (1) doesn't tell us how much more.
   Also, "help" in (1) and "increases" in (2) could be more specific; and "can help" is
   probably a weasel word—it sounds good but it leaves open the possibility that it
   won't help a particular person at all.


(1) Krufts are proud to announce their new LITE cottage cheese. Better for you than
    ever before!




(2) The mind is not just a physical brain, without any freedom. It's all in quantum
    theory.
                                                                                  Ex—37

(3) One teenager to another. Fertilizer must be good for the environment. Fertilizer helps
    grow trees, grass, bushes, and flowers. Trees, grass, bushes and flowers are the
    environment. So, fertilizer is good for the environment.




(4) You should buy the recent phenomenon sweeping the world, The Secret. There are
    several reasons you should buy the book, The Secret. The first and most important is
    that it contains the knowledge to achieve eternal happiness and success in life,
    whatever your goals. A number of metaphysicians and visionaries all agree that it
    contains true and proven methods to bring yourself success and happiness. What's
    holding you back?




(5) Bill:    I think bio-diesel fuel is the future.
    Henry:   Oh really. How do you know this?
    Bill:    Well, I read it in some magazine
                                                                                   Ex—38

(6) At the fair-ground: Unfortunately, young man, because you are vertically challenged,
    you cannot get on this ride.




(7) In court: But your Honor, this sentence is unfair. I was only engaged in a spot of
    commodity relocation across the border.




(8) In court: Of course my pamphlet counts as a book and is therefore protected under
    Code 17 of the copyright law. After all, this book I have in my hands has only 50
    pages, and would still be a book if I took away one leaf, thus reducing it to 48 pages.
    And it would still be a book if it had 46. And so on, until we reach 8 pages, which is
    how many my pamphlet has. It is thus a book.
                                                                                 Ex—39

An Introduction To Reasoning
Exercise Set (2) on Getting Clear On The Meaning (4.2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. Then, (vi) discuss any
issues concerning the meaning of the reasons and target.

(1) You should drink a Schnapp's Ginger Ale today. New Schnapp's Ginger Ale
    contains anti-oxidants, which as everyone knows are healthy for you.




(2) If you want 6-pack abs without hitting the gym, look no further! The new Sport-
    Select belt is your answer. The belt sends tiny micro shocks into your abdominal
    muscles that causes them to flex and unflex. Studies have shown a toner, more
    muscular mid-section in just two weeks. So, if you are tired of doing crunches and
    sit ups, order the Sport-Select belt today for guaranteed results!




(3) Shop at Wal Mart. They have unbeatable prices. What other reason do you need?
                                                                                     Ex—40

(4) Gill is thinking about her diet. Nabisco is now offering sugar-free Twinkies. So, I guess
    Twinkies can now be included as part of my diet along with lettuce and carrots.




(5) Jack:     I think we should buy some home-style mashed potatoes instead of
              regular.
   Gill:      Why? Are they any better?
   Jack:      Well, my mother use to make the best tasting mashed potatoes ever, and if
              these are home-style they must be like hers.




(6) State Farm. The reasons to get a quote just keep adding up.
                                                                                     Ex—41

(7) A new agenda is needed for Congress. Scott Taylor has that agenda. He has been a
    Navy Seal and has seen the problems of the world first-hand. He has what the U.S.
    needs.




(8) A new report describes how Bisphenol-A can leach from water bottles into the liquid
    in the water. For this reason, then, it is advisable to use a ceramic or metallic bottle.




(9) Henry speaks: Acting justly is doing what benefits the stronger person. Since
    Poludamas the wrestler is stronger than I am, and he eats 10 pounds of meat a day, I
    eat 10 pounds of meat per day. (Based on Plato, Republic 1)
                                                                               Ex—42

(10) Henry is taking a critical reasoning course. Being critical of others often makes
    them upset. So, Henry's course is on how to make others upset.




(11)   Smith: The Founding Fathers never intended that illegals could sneak across the
              border and have "anchor babies". Thus, changing the 14th amendment
              would not be unconstitutional.
       Jones: But these undocumented workers are vital to the U.S. economy!
                                                                                   Ex—43

An Introduction To Reasoning
Exercise Set (1) on Sources (4.3)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Give a diagram. (vii)
Discuss the credibility of the source(s) appealed to.

Sample
     Jack: I heard on the Weather Channel this morning that temperatures today will
     reach 100 degrees in coastal areas. So, you might want to postpone moving until
     this evening.

       Jack appeals to the Weather Channel, which reports the weather. Although it
       doesn't explain how it arrives at forecasts, its track record establishes it as both
       an authority and trustworthy, with respect to weather.

(1) My hair stylist told me that honey speeds up your metabolism and so that it is good
    for you.




(2) U.S. News & World Report report that honey is good for you. It speeds up your
    metabolism.




(3) The New York Times reports that honey is good for you. It speeds up your
    metabolism.
                                                                                 Ex—44

(4) I, the mayor of Birmingham, endorse Scott Taylor for Congress. Please vote for him.




(5) The Pope, an authority on such matters to millions of Catholics world-wide, claims
    that in heaven we will have genitalia but we will not be using them. So that's how it
    will be.




(6) Jack:    You believe in Zeus and Hera?!
    Gill:    Of course! My parents told me to believe in them.
                                                                                  Ex—45

(7) The Bible says it's okay to own slaves, so long as they're from another country. So, I
    guess slave-ownership is okay.




(8) The National Enquirer's top story this week is about an alien invasion during the
    Reagan administration. Apparently, Reagan's body had been taken over by aliens.




(9) My dentist, Dr. Holmes, said that the key to producing unlimited energy using
    nuclear fusion at room temperature is the creation of muonic atoms of tritium. You
    can't doubt a medical doctor on these things.
                                                                                 Ex—46

An Introduction To Reasoning
Exercise Set (2) on Sources (4.3)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Give a diagram. (vii)
Discuss the credibility of the source(s) appealed to.

(1) Bill:     I think bio diesel fuel is the future.
    Henry:    Oh really. How do you know this?
    Bill:     Well, I read in Time magazine as well as National Geographic what exactly
              bio-diesel is capable of.




(2) Smith: I believe that global warming is real. This has been the hottest summer I have
    ever seen.




(3) A TV Ad: Miley Cyrus says "Wal-Mart is a great place to shop."
                                                                              Ex—47

(4) James Johnston, president of R. J. Reynolds Tobacco Company, maintains that
    tobacco isn't physically addictive, and that thus his company's cigarettes aren't
    physically addictive either. He is obviously an expert in this area, and so it's
    probably true that tobacco or cigarettes aren't physically addictive.




(5) Gill:    Not all elephants get scared by mice, like cartoons like to portray.
    Jack:    How do you know this?
    Gill:    I was at the circus last week and they had mice in the ring with the
             elephants and they were calm.




(6) Bill:    Who are you voting for in the up-coming mayoral election?
    Henry:   I'm voting for the Labour candidate.
    Bill:    Why is that?
    Henry:   My parents have always voted Labour, so I guess I will too.
                                                                                    Ex—48

(7) A paleontologist friend of mine says evidence against humans co-existing with
    dinosaurs is strong and well-known to the scientific community.




(8)   Smith: Hey Jones, you should collect your old and broken gold to sell to Goldline
             International. According to their experts, gold is selling at an all time high.
             Goldline International is even offering a bonus of 10% right now!
                                                                                   Ex—49

An Introduction To Reasoning
Exercise Set (1) on Reason Substitutes (4.4)

Discuss each passage or dialogue in terms of missing the target.

Sample
   Jack:      IPCC reports show that global warming will continue to increase in the
              foreseeable future, leading to increasingly erratic weather patterns.
    Gill:     Yes, and maybe pigs will fly, too.

    Gill has responded by ridiculing the idea Jack presents, but she has not actually
    given an objection.

(1) Don Stewart:     This show is hurting the political discourse in America. Please stop.
    Buck Carlson:    Well, what about you? On your show you asked John Kerry "How
                     are you holding up?"! (Based on Jon Stewart on Crossfire)




(2) Gill:     I'm boycotting Target because they give campaign donations to anti-gay
              candidates.
    Jack:     Well, it's a free country. You can do whatever stupid thing you like.




(3) Jack:     You believe in Zeus and Hera?!
    Gill:     Of course! Only an amoral fool could deny their existence!
                                                                             Ex—50

(4) Bill:    People should adopt puppies from shelters rather than buying from
             puppy-mills.
    Henry:   Wow, I knew you were dumb, but that really takes the cake.




(5) Jack:    I don't think OJ committed those murders.
    Gill:    What makes you think that?
    Jack:    Well, why would he commit them? "Innocent until proven guilty", you
             know.




(6) Smith:   Who are you voting for in the up-coming mayoral election?
    Jones:   I'm voting for the Republican candidate.
    Smith:   Why is that?
    Jones:   Well why not?




(7) Opium puts people to sleep because of its dormitive power.
                                                                                  Ex—51

An Introduction to Reasoning
Exercise (2) on Reason Substitutes Really Bad Reasoning (4.4)

Exercise (1) was too easy. Here is a selection of passages involving really bad reasoning,
but they are not always of the kinds described in 4.4. Thus, you will have to find your
own words in order to describe what makes (some of) these so bad.

(1) A pit bull enthusiast to her friend. Pit bulls are not aggressive dogs. Our neighbors'
    black lab has bitten several people and has also had to undergo doggy obedience
    classes. He even killed a cat!




(2) Smith:   I strongly believe that dinosaurs went extinct due to an asteroid hitting
             the earth. The impact would have put tons of dust into the air, blocking
             the sun, leading to loss of plant life. With out plants, the herbivores died.
             Without herbivores, the carnivores died and so on.
    Jones:   Wow, that sound like something my eight-year-old sister would say. How
             about a good theory next time?




(3) Gill:    Using animals for our own benefit is immoral. We should all become
             vegans and cease using animals products.
    Jack:    What about you? You're wearing a leather belt!
                                                                                      Ex—52

(4) Smith:    Tom DeLay says that the U.S. must take action against Iran's nuclear
              program, because it poses a threat to stability in the Middle East.
   Jones:     I don't need to pay attention to anything that crook says.




(5) Jack:     The president's new universal health-care initiative will be good for the
              nation.
   Gill:      The plan sounds suspiciously like something Hitler would do. (Based on
              the Dave Barry column How To Win Any Argument)




(6) Jack is pleading to keep his post: Sir, if you relieve me of my duties, I won't be able to
    pay my rent and my room-mate will have to move. And my cat is really sick and the
    vet is incredibly expensive. You wouldn't want a poor innocent cat to die!
                                                                                     Ex—53

(7) We don't know that ghosts don't exist. Until there is definitive proof, then, it seems
    reasonable to believe in them.




(8) On the campaign trail: My opponent says that immigration law must be reformed in
    order to allow illegal immigrants a chance to become legal. But he neglects the plight
    of the working poor already living in this country. We are in the middle of the
    deepest recession in 20 years. Many people are unemployed and families have
    expended their savings and are dipping into mortgage equity and retirement
    accounts.




(9) At a crime-scene: Move along folks. There's nothing to see here. I'm a police officer.
                                                                                Ex—54

(10) At a bay: For over a hundred years now, my family has been harvesting these
    oysters to make a living. Oyster farming is a family tradition, and so we should be
    allowed to keep harvesting, even though the oyster fields are in danger of being
    destroyed.
                                                                                   Ex—55

An Introduction To Reasoning
Exercise Set (1) on the Two Criteria (4.5)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Give a diagram.
Then (vii) evaluate the truth of the reasons, given your current knowledge, (vii)
evaluate the reasoning and (ix) given your answers to (vii) and (viii) say whether the
(initial) argument or explanation is good.

Sample:
   John McCain says that George Bush deserves "some credit" for recent (August 2010)
   developments in Iraq. I'll give Bush "some credit" for developments in Iraq just as
   soon as you give him "some blame" for the economy. (Based on
   http://www.washingtonmonthly.com/archives/individual/2010_08/025279.php)

(1) Bush does not deserve some credit for developments in Iraq.                2
(2) McCain is selective in ascribing praise and blame to Bush.
                                                                           J

                                                                               1

Reasons?:   I know nothing about McCain's pronouncements beyond this passage.
Reasoning?: Even if McCain is selective in giving Bush praise and blame, his
            inconsistency is irrelevant to the issue at hand.
Overall?:   Not convincing.

(1) Gloaming was the top selling fiction book of 2009 in the UK. Therefore, it was the
    best work of fiction of 2009 in the UK.




(2) Arguing about the IPL. The Mumbai Indians have a lot of star players on their team.
    So, they are a great team.
                                                                                   Ex—56

(3) A third of Americans are obese and 10% of healthcare costs are spent on obesity-
    related issues. It's clear that we must tackle the obesity problem. (Data as reported
    by NBC Nightly News 2010-08-04)




(4) A pit bull enthusiast to her friend. Pit bulls are not aggressive dogs. We have owned a
    pit bull for 10 years now and he has not harmed a flea. Our pit bull barked at
    someone once, but that was only because he was spooked by them.




(5) Smith:   I think bio-diesel fuel is the future.
    Jones:   Oh, really. How do you know this?
    Smith:   Well, gasoline power just seems so … yesterday to me. I think it's time for
             something new.
                                                                                Ex—57

(6) People think granola bars are healthy for you because they are low in fat and have
    ingredients such as oats and wheat which are good for your body. Some even
    contain fruit, another healthy ingredient.




(7) One student to another. I'm telling you, chocolate can be good for you. My
    grandfather starting eating one piece of dark chocolate a day when he had his first
    heart attack. The result was lowered cholesterol, cleaner arteries, and better
    breathing. It is all thanks to his daily chocolate supplement.




(8) Doing marijuana would be bad. You shouldn't do marijuana. (Based on South Park
    204):
                                                                                Ex—58

(9) A paleontologist at a dinosaur expo: Recent groups have been promoting the idea that
    humans co-existed with dinosaurs. As neat as that would be, no evidence has been
    found today to promote it. Evidence against it is strong. Using radioactive dating,
    the decay rate is measured and dinosaur fossils have never been found in any time
    period near human fossils. In fact, they are separated by millions of years.




(10) The majority of Americans are obese, which increases the risk of heart attack. The
    obesity is from eating a lot of fast food, which is high in sodium, trans fat, and
    saturated fat. So, if Americans stopped eating so much fast food, they would not
    have as many heart attacks.
                                                                                 Ex—59

An Introduction To Reasoning
Exercise Set (2) on the Two Criteria (4.5)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Give a diagram.
Then (vii) evaluate the truth of the reasons, given your current knowledge, (vii)
evaluate the reasoning and (ix) given your answers to (vii) and (viii) say whether the
(initial) argument or explanation is good.

(1) Vitamins are good for you. Croke Plus now has vitamins in it. Croke Plus is good for
    you. Croke Plus is a soda, and so, sodas are good for you. Therefore, Sprice is also
    good for you.




(2) The new Xbox 360 is a better buy than the PlayStation 3. It comes with a built-in
    wireless adapter, which you have to buy separately for the PlayStation. It also comes
    with a built-in 250 gig hard drive, which is more than the PlayStation 3 offers.
    Finally, it comes ready to hook up its motion sensor adaptor for movement-based
    games, which PlayStation does not have at all.
                                                                                   Ex—60

(3) Everyone should buy a vehicle made by KIA motors. They are offered at an
    affordable price, they are very fuel efficient, and come in a variety of colors. They
    also have great warranties. Buy one today!




(4) One young child to another. It's amazing: My dog only eats things that are good for
    him. For example, the other day, he would not eat chocolate. But when offered some
    vegetables, he ate them all. He is eating grass right now. So, it must be good for him.




(5) Fertilizer helps grow trees, grass, bushes, and flowers. Trees, grass, bushes and
    flowers are the main things in my garden. So, fertilizer helps my garden.
                                                                                    Ex—61

(6) Jack to Gill: I am voting for Smith in the next election. I may not know a lot about his
    political views, but I know his faith. I agree with his faith so I will vote for him.




(7) Jack:     Did you hear that huge rainstorm last night?
    Gill:     Sure. It was impossible to miss.
    Jack:     I think it was what caused me to be late for work this morning.
    Gill:     Oh really? Wasn't it rather that you stayed up until 2 playing WoW?




(8) There are several reasons why we should start to invest in bio-diesel. First, studies
    have found that it is completely biodegradable, and less toxic than table salt. It has
    also passed all health effects testing, unlike all other fuels. Finally, it can made,
    shipped, and sold locally and so we won't have to rely on other countries for energy.
    The farming and selling of the plants it comes from would also boost the economy.
                                                                                   Ex—62

(9) A large part of human milk cannot be digested by babies. … The [indigestible]
    complex sugars were long thought to have no biological significance, even though
    they constitute up to 21 percent of milk. However, it now appears that they do have
    a purpose. [A] particular strain of bacterium, a subspecies of Bifidobacterium
    longum, possesses a special suite of genes that enable it to thrive on the indigestible
    component of milk. … It coats the lining of the infant's intestine, protecting it from
    noxious bacteria.
       (Based on http://www.nytimes.com/2010/08/03/science/03milk.html )




(10) The U.S. government will give a $7,500 tax credit to drivers who buy new electric
    cars such as the Nissan Leaf or Chevy Volt, hoping to reduce national gasoline
    consumption. This is simply yet another example of industry favoritism by the
    government. Why should the government favor plug-ins? It should simply raise the
    gas tax and let the markets decide.
    (Based     on      http://www.usatoday.com/news/opinion/editorials/2010-08-03-
    editorial03_ST_N.htm )
                                                                                   Ex—63

An Introduction To Reasoning
Exercise Set (1) on Adding Warrants (4.6)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Give a diagram.
Next, make the line of reasoning explicit by (vii) adding in writing any missing
propositions, marked with an asterisk. Add the new premises also to your diagram.
(viii) Say whether the reasons, including any you added, are true, as far as you know.
Add explanations at any point if necessary.

Sample
   What a scumbag! Thomson deliberately caused the accident and then sued the
   other driver.

      (1) Thomson is a scumbag.                                        2 + 3 +4
      (2) Thomson deliberately caused the accident.
      (3) Thomson sued the other driver.
      (4) People who cause accidents in order to sue others are         1
              scumbags.*

      The additional premise seems good to me (though "scumbag" is a somewhat vague
      term).

(1)   We don't know that ghosts don't exist. So, it seems reasonable to believe in them.




(2)   The statue sank because it is made of bronze.
                                                                                  Ex—64

(3)   I was late to class because traffic was terrible.




(4)   Everywhere I go those days, I see people on their mobile phones. So, I guess almost
      everyone has one these days.




(5)   Palin was a terrible pick for vice presidential candidate. She didn't know the first
      thing about most political issues.
                                                                               Ex—65

(6)   Stocks fell today on news that first-time claimants for unemployment benefits
      reached their highest total in the year to date.




(7)   Wyclef Jean has been blocked from running for the Haitian presidency because he
      is not a resident of the country.




(8)   The international community feels secure in allowing Iran to beginning producing
      nuclear power because the fuel is low-enriched uranium, which comes from
      Russia, which is also where the spent uranium will return, and that the process
      will    be    watch    closely     by     the    UN's     atomic     agency.   (
      http://www.bbc.co.uk/news/world-middle-east-11046174 )
                                                                                     Ex—66

An Introduction To Reasoning
Exercise Set (2) on Adding Warrants (4.6)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the reasons, (iv) make note of any needed changes or write
out the propositions in full, and (v) number the propositions. (vi) Give a diagram.
Next, make the line of reasoning explicit by (vii) adding in writing any missing
propositions, marked with an asterisk. Add the new premises also to your diagram.
(viii) Say whether the reasons, including any you added, are true, as far as you know.
Add explanations at any point if necessary.

(1)   The book Jack is looking for is on his desk. So, the book is on the second floor.




(2)   Christopher Hitchens got cancer because he does not believe in the Christian god.




(3)   Jack is in the army because he is patriotic.
                                                                                    Ex—67

(4)   I [Jack] need to get there as quickly as possible. I guess I should take the freeway,
      even though there is a toll.




(5)   Critics everywhere are calling Deception the best movie of the year. See it today at a
      theatre near you.




(6)   Australian markets are set to lower open this morning after the very close election
      which has left the country facing a hung parliament.
                                                                                    Ex—68

(7)   Ground Zero is a sacred site. There's no way that a mosque can be built anywhere
      near it.




(8)   Gill hasn't returned my calls or texts but I know she is in town. I think she avoiding
      me. I think it's because I said her argument about animal welfare was bogus.




(9)   The Zagat survey results released Monday indicate the upstart chain [Five Guys
      Burgers and Fries] has supplanted its cult-favorite predecessor in the Best Burger
      category … When I pressed [the owner] on why Five Guys was winning … he
      says: "The fresh ground beef and unlimited fresh and interesting toppings has
      caught the public imagination and taste."
      (http://www.dailyfinance.com/story/company-news/five-guys-new-burger-
      masters/19595634/ )
                                                                                   Ex—69

An Introduction To Reasoning
Exercise Set (1) on Valid, Cogent, Incogent (5.1-3)

Part 1. Underline "T" for true and "F" for false.

(1) You cannot judge an argument as sound and refuse to accept its conclusion.

   T          F

(2) It is impossible to have a valid argument with a false premise.

   T          F

(3) Every argument with true premises is sound.

   T          F

(4) A cogent argument with false premises is unsound.

   T          F

(5) It is impossible to have a valid argument with a false premise.

   T          F


Part 2. For each argument, (i) say whether the argument is valid, cogent, or incogent, (ii)
say whether, based on your current knowledge, all the premises are true, and (iii) based
on your answers to (i) and (ii) say whether the argument is sound or unsound. Explain
your answer to (i) and (ii). If your answer to (ii) is "no" because you don't know, say
what you would need to know and how you would find out.

Sample

   The patient has a red rash covering the extremities and head, but not the torso. The
   only cause of such a rash is a deficiency in vitamin K. So, the patient has a vitamin K
   deficiency.

(i) Valid. The word "only" means it must be vitamin K deficiency.

(ii) No. Because I don't know anything about the effect of lack of vitamin K. I would
consult a doctor or medical encyclopedia.

(iii) Unsound.
                                                                                Ex—70

(6) On 2003/06/19 in Norfolk, VA, a violent storm blew through and the power went
    out over much of the city. So, the storm caused the power to go out.




(7) Elvis Presley was also known as 'The King'. Elvis had 18 songs reach #1 in the
    Billboard charts. So, The King had 18 #1 hits.




(8) Most philosophers are right-handed. Terence Irwin is a philosopher. So, he is right-
    handed.




(9) The Ohio State football team beat the Miami football team on 2003/1/3 for the
    college national championship. So, the Ohio State football team was the best team in
    college football in the 2002-3 season.
                                                                                Ex—71

(10) Willie Mosconi made every shot he took in 1941. For he made almost all of the
    pool shots he took from 1940-1945, and he took a bunch of shots in 1941.




(11) Flyers must submit to either a full-body scan or a thorough pat-down. Attempts
    have been made recently to carry bombs or bomb-making materials onto planes in
    the underwear and in other personal areas. These types of procedure provide a large
    measure of security against such attempts.
                                                                                   Ex—72

An Introduction To Reasoning
Exercise Set (2) on Valid, Cogent, Incogent (5.1-3)

Part 1. Underline "T" for true and "F" for false.

(1) A cogent argument with true premises is sound.

   T          F

(2) No cogent argument is sound.

   T          F

(3) Every incogent argument is invalid.

   T          F

(4) Every unsound argument is either invalid or incogent.

   T          F

(5) Every invalid argument is unsound.

   T          F




Part 2. For each argument, (i) say whether the argument is valid, cogent, or incogent, (ii)
say whether, based on your current knowledge, all the premises are true, and (iii) based
on your answers to (i) and (ii) say whether the argument is sound or unsound. Explain
your answer to (i) and (ii). If your answer to (ii) is "no" because you don't know, say
what you would need to know and how you would find out.


(6) In all likelihood, Jack's dog Jim will die before the age of 73 (in human years). After
    all, you are familiar with lots of dogs, and lots of different kinds of dogs, and any
    dog that is now dead died before the age of 73 (in human years).
                                                                                   Ex—73

(7) Any time the public receives a tax rebate, consumer spending increases, and the
    economy is stimulated. Since the public just received a tax rebate, consumer
    spending will increase.




(8) 90% of the marbles in the box are blue. So, about 90% of the 20 I pick at random will
    be blue.




(9) According to the world-renowned physicist Stephen Hawking, quarks are one of the
    fundamental particles of matter. So, it's likely that quarks are one of the fundamental
    particles of matter.
                                                                               Ex—74

(10) Sean Penn, Susan Sarandon and Tim Robbins are actors, and Democrats. So, in
    all likelihood, most actors are Democrats.




(11) The President's approval rating has now fallen to 53%, employment is at a 10
    year high, and he is in charge of two foreign wars. There would be no way he would
    win another term in two year's time, if he were to run.
                                                                                   Ex—75

An Introduction To Reasoning
Exercise Set (1) on Valid, Cogent, Incogent and What The Arguer Thinks (5.4)

For each argument, (i) say whether the arguer thinks the inference is valid or cogent (or
neither) and underline the words (if any) on which you are basing your answer, (ii) say
whether the argument is valid, cogent, or incogent (discuss as necessary), (iii) say
whether, based on your current knowledge, all the premises are true (if "no" because
"don't know" say how you would find out), and (iv) based on your answers to (ii) and
(iii), say whether the argument is sound or unsound.

Sample

   The sun has come up in the east every day in the past. So for sure, the sun will come
   up in the east tomorrow.

(i) Necessarily. Based on the words "for sure".

(ii) Cogent. Extremely likely, but not guaranteed, since the future might be different.

(iii) Yes. No human has seen the sun every day in the past, but it seems reasonable to
believe that it has been around for as long as Earth has.

(iv) Sound.

(1) All men are things with purple hair, and all things with purple hair have nine legs.
    Therefore without a doubt, all men have nine legs.




(2) There are exactly 10 humans in Carnegie Hall right now. Every human in Carnegie
    Hall right now has exactly ten legs. And, of course, no human in Carnegie Hall
    shares any legs with another human. Thus certainly, there are at least 100 legs in
    Carnegie Hall right now.
                                                                                   Ex—76

(3) Jack has purple hair, and purple toe nails. Hence without a doubt, he has toe nails.




(4) Some philosophers are people who are right-handed. We can be sure therefore, that
    some people who are right-handed are philosophers.




(5) (U.S.) President Bush firmly believed that there were WMDs in Iraq. We can
    conclude with certainty thus, that there were WMDs in Iraq.




(6) Since the Spanish American War occurred before the American Civil War, and since
    the American Civil War occurred after the Korean War, it follows for certain that the
    Spanish American War occurred before the Korean War.
                                                                                 Ex—77

(7) Amy Bishop is an evolutionary biologist and shot her colleagues to death (in 2010).
    Evolutionary biology is incompatible with [Christian] scriptural teaching, and
    scriptural teaching is the only grounding for morality. It's likely, then, that
    evolutionary biology predisposes people to commit murder by shooting their
    colleagues to death.




(8) I [Socrates] can't possibly have corrupted my associates intentionally, since corrupt
    people do harm to those around them, and no one intentionally wants to be done
    harm.




(9) Taxation means giving some of your earned income to the government. Some of this
    income is distributed to others. Being forced to work so that someone else can
    benefit is slavery. Therefore, taxation is slavery.
                                                                                      Ex—78

An Introduction To Reasoning
Exercise Set (2) on Valid, Cogent, Incogent and What The Arguer Thinks (5.4)

For each argument, (i) say whether the arguer thinks the inference is valid or cogent (or
neither) and underline the words (if any) on which you are basing your answer, (ii) say
whether the argument is valid, cogent, or incogent (discuss as necessary), (iii) say
whether, based on your current knowledge, all the premises are true (if "no" because
"don't know" say how you would find out), and (iv) based on your answers to (ii) and
(iii), say whether the argument is sound or unsound.

(1) If Bill Gates owns a lot of gold then Bill Gates is rich, and Bill Gates doesn't own a lot
    of gold. So, Bill Gates probably isn't rich.




(2) All birds have wings, and all vertebrates have wings. So, it's likely that all birds are
    vertebrates.




(3) (U.S.) President Obama gave a speech in Berlin shortly after his inauguration. Berlin,
    of course, is where Hitler gave many speeches. It's thus likely that Obama intends to
    establish a socialist system in the U.S.
                                                                                Ex—79




(4) The United States Congress has more members than there are days in the year. It is a
    certainty thus, that at least two members of the United States Congress celebrate
    their birthdays on the same day of the year.




(5) Einstein said that he believed in a god only in the sense of a pantheistic god
    equivalent with nature. Thus, there must not be any god in the Christian sense.




(6) Guantanamo ought to be closed on the grounds that the continued incarceration of
    prisoners without any move to try or release them provides terrorists with an
    effective recruiting tool.
                                                                                Ex—80

(7) Smith and Jones surveyed teenagers (13-19 years old) at a local mall and found that
    94% of this group owned a mobile phone. It was therefore likely, they concluded,
    that about 94% of all teenagers own mobile phone.




(8) Shellie Ross is obviously an unfit mother. She sent so many tweets in the time prior
    to the drowning of her son—any parent who spends this much time on Twitter
    when they have kids is not giving them proper attention.
                                                                                    Ex—81

An Introduction To Reasoning
Exercise Set (1) on Adding Warrants To Arguments (5.5)

For each argument, (i) underline the conclusion, (ii) put any flag words in parentheses,
(iii) make note of any changes made at this stage, (iv) give a diagram. Next, make the
line of argument explicit by (v) adding a warrant(s), marked with an asterisk. Add the
new premises also to your diagram. Say whether the premises, including any you
added, are true, as far as you know. Add explanations at any point if necessary.

Sample

       Potatoes are vegetables, (so) potatoes are good for you.

   1. Potatoes are vegetables.                                        (1 + 3)
   2. Potatoes are good for you.

   3. Vegetables are good for you.*
                                                                       2

(vi) Valid
(vii) True

(1) Nozick's thought experiment shows us that we value authenticity (i.e. that the life
    we lead is a real one and not a virtual reality). So, a life without authenticity cannot
    be a satisfactory one.




(2) Humans in Persistent Vegetative State (PVS) should not be euthanized. After all,
    they are still persons.
                                                                                  Ex—82

(3) Watching TV does not cause violence. If it did, there would be more than ten million
    acts of violence every week.




(4) A student is talking to an instructor: I didn't turn in my homework on time because my
    dog took sick and I had to take her to the vet. So, you should not penalize me for
    turning it in late.




(5) George Bush believes that the sun will rise in the east tomorrow. We can conclude
    with certainty thus, that George Bush knows that the sun will rise in the east
    tomorrow.
                                                                               Ex—83

(6) (Consider only the underlined portion of the following:) My dog Jim is smart. He
    was chasing a rabbit, which rounded a corner and went down the left-hand path at a
    fork in the path. Jim sniffed the right-hand path and set off down the left. He
    reasoned that since the rabbit hadn't gone to the right, it had gone to the left.




(7) Children often get into accidents because they are mischievous and curious.
    Accidents should be prevented. So, children should be supervised at all times.
                                                                                    Ex—84

An Introduction To Reasoning
Exercise Set (2) on Adding Warrants To Arguments (5.5)

For each argument, (i) underline the conclusion, (ii) put any flag words in parentheses,
(iii) make note of any changes made at this stage, (iv) give a diagram. Next, make the
line of argument explicit by (v) adding a warrant(s), marked with an asterisk. Add the
new premises also to your diagram. Say whether the premises, including any you
added, are true, as far as you know. Add explanations at any point if necessary.

(1) Many illegal immigrants are paid less even though they perform the same jobs as
    citizen. So, they should be paid just as much as their legal counterparts.




(2) The Patriots haven't lost a game so far this season, so they will not lose the
    Superbowl game on Sunday.




(3) Simple-minded people will interpret the results of the recent prayer study to mean
    that there is no God and morality is necessary to society. So, the results of the recent
    study threaten society.
                                                                                  Ex—85

(4) I would argue that people do not seem to keep track of the justifications of their
    beliefs. If we try to suppose that people do keep track of their justifications, we
    would have to suppose that either they fail to notice when their justifications are
    undermined or they do notice but have great difficulty in abandoning the
    unjustified beliefs in the way a person has difficulty abandoning a bad habit. Neither
    possibility seems plausible.




(5) We should prohibit anything that causes accidents on the nation's highways. Thus,
    the use of mobile phone while driving should be prohibited.




(6) The Virginia Tech. massacre was a terrible tragedy. We should do everything we can
    to prevent such tragedies. Concealed weapons should be allowed on college
    campuses.
                                                                                       Ex—86

(7) If we turn up the heat, the electricity bill will be high. So, if we turn up the heat, we
    won't be able to afford the cable bill.




(8) After decades without a change, Campbell's soup is moving away from its classic
    label. It's clear that sales will go up in the short term, prior to the introduction of the
    new label.
                                                                                                          Ex—87

An Introduction To Reasoning
Exercise Set (1) on Inductive Generalization (6.2)

For each argument, (i) put the argument in standard form, including any information
about the size and representativeness of the sample (if there is no information, insert as
missing premises the generic warrants needed to make the argument cogent; (ii) discuss
the size and representativeness of the sample.

Sample

    In a recent survey of 500 randomly selected prisoners in various North American
    prisons, 28% claimed that they were in fact innocent of the crimes they had been
    charged with. This leads me to believe that about 28% of the continent's prison
    population would claim to be innocent.

1. 28% of surveyed prisoners in various North American prisons claimed that they were
    in fact innocent of the crimes they had been charged with.
2. The sample, 500 prisoners, is large enough.*
3. The sample, taken randomly from the prison population, is unbiased.*
    ----------------------------------------------------------------------------------------------------------------
4. About 28% of North America's prison population claims to be innocent of the crimes
    they were charged with.

(ii) Size: Whether 500 is large enough will depend on the size of the prison population,
     which I do not know. If it is millions of people, 500 is not enough.
     Representativeness: The sample is random (though we're not told the mechanism).



(1) On Dec. 1, 2005, a phone-in poll of 404 Fox News viewers found that 87% of
    respondents believed that schools, courthouses and other government buildings
    should be allowed to display Christian Christmas imagery. We can conclude,
    therefore, that about 87% of all Fox News viewers believe this.
                                                                                    Ex—88

(2) On our first date, George had his hands all over me, and I found it nearly impossible
    to keep him in his place. Then a week ago Tom gave me that stupid line about how,
    in order to prove my love, I had to spend the night with him. I bet almost all men
    are like that: all they want is sex.




(3) In the last year, we had 10 storms here at Norfolk Horse. In 9 of those 10
    thunderstorms, at least one horse kicked its stall. So, at least one horse will kick its
    stall in about 90% of future storms here.
                                                                                    Ex—89

(4) 95% of Criminal Justice majors at Harvard university find employment upon
    graduating. So, CJ graduates generally have a good chance of becoming employed.




(5) Quality control at the TV factory producing roughly 30,000 unit per annum consists
    in testing 2% of televisions coming off the line for defects. Of these, 99% are found to
    be sound. So, about 99% of all the televisions produced there are sound.




(6) The New York Times reports ('A Depression Switch?' David Dobbs, April 2, 2006) that
    8 of 12 patients in a trial study have responded to Deep Brain Stimulation, a
    treatment for people with depressions resistant to antidepressants, anti-anxiety
    drugs, intensive psychotherapy and electroconvulsive therapy. So we can conclude
    that two-thirds of people with such depressions will be aided by DBS.
                                                                                  Ex—90

An Introduction To Reasoning
Exercise Set (2) on Inductive Generalization (6.2)

For each argument, (i) put the argument in standard form, including any information
about the size and representativeness of the sample (if there is no information, insert as
missing premises the generic warrants needed to make the argument cogent; (ii) discuss
the size and representativeness of the sample.

(1) 75% of the wild ponies we have rounded up from Chincoteague island are some
    shade of brown. Therefore, about 75% of all wild ponies on the island are some
    shade of brown.




(2) In a recent LA Times poll of 180 people interviewed as they left a Raiders (American
    football) game, 72% were against admitting China to the United Nations, and so it
    follows with high probability that approximately 72% of all adults in the United
    States are against admitting China to the United Nations.
                                                                                   Ex—91

(3) In order to test the boiling point of water at a given altitude, we took a liter of tap
    water to 700 feet, heated it to boiling and measured it with a scientific thermometer.
    We also collected a liter of water from a stream on the mountain. The boiling point
    in both cases was found to be 99.4 degrees Celsius. So, all water at this height will
    boil at roughly this temperature.




(4) A small college of 1,200 students recently surveyed its undergraduate degree
    students using a Student Satisfaction Inventory. The survey was made available to
    students on-line (via Blackboard), and those completing the survey (and giving their
    name, confidentially) were entered in a prize drawing. There were 449 total
    respondents. Of these, 304 were female, 142 male (3 did not answer this item). 314
    were White Caucasian, 71 were African-American, 13 Hispanic, 11 Asian and 40
    belonged to other races or did not answer. By class rank, 134 Freshmen, 124
    Sophomores, 96 Juniors and 94 Seniors completed the survey (1 did not answer).
    Results showed that 85% were 'satisfied' or 'very satisfied' with campus life, while
    92% were 'satisfied' or 'very satisfied' with the academic program. Thus, about the
    same percentage of the whole student body holds these views.
                                                                               Ex—92

(5) Reconstruct and comment on the inference described in the following: Asked why
    he tosses coins into wells, ponds and other bodies of water, the subject responded
    that once a wish (concerning a sports bet) that he had made previously after
    throwing a coin into a well had come true in dramatic fashion.




(6) Reconstruct and comment on the inference in the following: Airline traffic fell
    dramatically after 9/11. Many people concluded that airplanes were dangerous to
    fly on.
                                                                               Ex—93

(7) Reconstruct and comment on the inference described below of a famous poll. What
    went wrong?

      Over the years Literary Digest had developed a sizable mailing list. … The
      magazine launched its largest survey ever in 1936. Going beyond its own mailing
      list, Literary Digest also added names from auto registration lists and telephone
      directories … Considerable time and expense had to be devoted to tabulating the
      flood of 2.4 million ballots returned. When they were all in, the magazine
      predicted that Alf Landon would carry 32 states and defeat Roosevelt by 57% to
      43%.
               The Digest was sorely embarrassed by the final outcome, a 61% to 37%
      Roosevelt landslide that left Landon with only two states and eight electoral
      votes compared to Roosevelt's 523.
               (http://www.orspub.com/brief%20history.html).
                                                                                                          Ex—94

An Introduction To Reasoning
Exercise Set (1) on Instantiation Syllogism, Induction to a Particular (6.3-4)

For each argument, (i) put the argument in standard form, including the warrants
needed to make the argument cogent; (ii) underline "IG" if it is an instance of inductive
generalization, "IS" if it is an instance of instantiation syllogism, "IP" if it is an instance
of induction to a particular; (iii) discuss whether the warrants are true; (iv) if the
argument is incogent, explain why.

Sample

    In a recent survey of 500 randomly selected prisoners in various North American
    prisons, 28% claimed that they were in fact innocent of the crimes they had been
    charged with. This leads me to believe that about 28% of the continent's prison
    population would claim to be innocent.

        IG       IS       IP

1. 28% of surveyed prisoners in various North American prisons claimed that they were
    in fact innocent of the crimes they had been charged with.
2. The sample 500 prisoners is large.
3. The random sample is unbiased.
    ----------------------------------------------------------------------------------------------------------------
4. About 28% of the North America's prison population claims to be innocent of the
    crimes they were charged with.

(iii) We do not know the details of the selection process, but random selection is good.
500 is a decent, though not very large, sample for a population of millions of people.

(1) The vast majority of people with an advanced case of lung cancer will die from the
    disease at some point within the next five years, and our good friend Henry has an
    advanced case of lung cancer. Unfortunately then, our good friend Henry will
    probably die from the disease at some point during the next five years.

        IG       IS       IP
                                                                                   Ex—95

(2) Almost every show in the past year that I've seen at the NORVA (concert hall), I
    liked. I am going to see a show on Friday. In all probability, I will like it.

       IG     IS     IP




(3) Lottery-winners are disproportionately male—about 65%. Last week's lottery had a
    winner. So, the winner of last weekend's jackpot was probably male.

       IG     IS     IP




(4) 9 out of 10 of the wild ponies in the back of the barn are mean, meaning that they
    bite and kick, until they are broken and trained. Greta is a wild pony in the back. She
    will bite and kick until she is broken and trained.

       IG     IS     IP
                                                                                    Ex—96

(5) Whitney, Kate, and Brian use peer-to-peer services to get music for free because they
    do not like buying expensive CDs. Gabriel, Whitney, Kate, and Brian are all
    members of class of 2010. So, Gabriel probably uses also peer-to-peer services for
    this reason.

       IG     IS     IP




(6) The pizza in the cafeteria has been cold every day this week so far. It'll be cold today
    too, I [Henry] bet.

       IG     IS     IP




(7) 9 of the last 10 thunderstorms, at least one horse kicked its stall. A thunderstorm is
    predicted for tonight. At least one horse will kick its stall.

       IG     IS     IP
                                                                                Ex—97

(8) Jack's dog lives in North America. Jack's dog barks at the mailman. Jack lives in
    North America. So, Jack barks at the mailman.

      IG     IS     IP




(9) In the Bible, God has a head and body, a voice, emotions, hair and even a beard. All
    humans have a head and body, a voice, emotions, and hair, and some even have a
    beard. Since the power of God goes with these features, it stands to reason that
    humans must also have the powers of God—even if they don't know it.

      IG     IS     IP
                                                                                       Ex—98

An Introduction To Reasoning
Exercise Set (2) on Induction (6.2-4)

For each argument, (i) put the argument in standard form, including the warrants
needed to make the argument cogent; (ii) underline "IG" if it is an instance of inductive
generalization, "IS" if it is an instance of instantiation syllogism, "IP" if it is an instance
of induction to a particular; (iii) discuss whether the warrants are true; (iv) if the
argument is incogent, explain why.

(1) Maureen Venla, mayor of Ourtown, probably didn't vote for Bush. For she's a
    Democrat from California, and only 1.3% of Democrats from California voted for
    Bush.

       IG     IS     IP




(2) 11% of the customers at Weeping Creek mall who tried a sample of new Land-O-
    Lard bite-size bacon strips went on to purchase at least one packet of the produce.
    On this evidence we can assume that about 11% of all samplers will purchase some
    of the product.

       IG     IS     IP
                                                                                    Ex—99

(3) I reckon Jack isn't coming to the Bible study meeting tonight. He has missed the last
    two.

       IG     IS     IP




(4) I [Henry] haven't seen a Scorsese flick I didn't like. So, I'm sure to enjoy his latest,
    Shutter Island.

       IG     IS     IP




(5) Every loyal Canadian hopes for a Canadian win over the U.S. team in curling at the
    next winter Olympics. So, we know Gill is hoping for a Canadian win, since she's a
    loyal Canadian.

       IG     IS     IP
                                                                               Ex—100

(6) Mabel is a dancer who has been able to find regular work. Dancers face intense
    competition; 90% of those with regular work are the most talented dancers. So,
    Mabel is a talented dancer.

      IG     IS     IP




(7) When tested, the substance was found to have the chemical composition C21H23NO5.
    C21H23NO5 is heroin. So, this substance is heroin.

      IG     IS     IP




(8) Jack, Gill and Henry hate buying expensive CDs and are all high-school graduates in
    2010. Jack and Gill use music file-sharing services on-line. So, Henry probably does
    too.

      IG     IS     IP
                                                                                 Ex—101

(9) Lori is a dancer. Most dancers begin formal training at an early age—between 5 and
    15—and many have their first professional audition by age 17 or 18. Lori just had
    her first professional audition, so Lori is 17 or 18 and started formal training at an
    early age.

      IG     IS     IP
                                                                                   Ex—102

An Introduction To Reasoning
Exercise Set (1) on Correlation (7.2-3)

Part 1
For each passage, (i) give the relation used (or implied); (ii) by drawing a correlation
diagram, indicate whether you think the two types of thing are correlated or merely
related and estimate the strength of the correlation; and (iii) explain your answer to (ii).

Sample
   The plants died because Jack forgot to water them for 3 months.

   (i) Relation Used: Plants that are not watered for 3 months die.

  (ii) Diagram:
             0% |             Die                     |100%
No Water 3 mo. |-----------------------------------|±|
Water           |--------|±|

   (iii) Explanation: Some plants, such as cacti, can survive for long periods without
   water, but most cannot. On the other hand, plants which are watered sometimes still
   die, but at much lower rates than non-watered plants.

(1) The statue sank because it is made of bronze.




(2) Christopher Hitchens got cancer because he does not believe in the Christian god.
                                                                               Ex—103

(3) The Irish are happy because they always think about how things could always be
    worse.




(4) Jack has a cold because he took a walk right after he washed his hair, on a freezing
    cold day.




(5) These crackers are stale because they are past their sell-by date.
                                                                                 Ex—104

Part 2

Read the article at http://www.nytimes.com/2010/08/17/nyregion/17walk.html

(6) Draw a correlation diagram with precise percentages for the claim that male drivers
    are disproportionately responsible for accidents resulting in death or serious injury.




(7) Draw a correlation diagram for the claim that left turns are disproportionately
    responsible for accidents resulting in death or serious injury.




(8) Draw a correlation diagram for the claim that taxi and livery cabs are
    disproportionately not responsible for accidents resulting in death or serious injury.




(9) Draw a correlation diagram for any other claim mentioned in the article.
                                                                                   Ex—105

An Introduction To Reasoning
Exercise Set (2) on Correlation (7.2-3)

Part 1
For each passage, (i) give the relation used (or implied); (ii) by drawing a correlation
diagram, indicate whether you think the two types of thing are correlated or merely
related and estimate the strength of the correlation; and (iii) explain your answer to (ii).

(1) I couldn't print out my paper because my printer at home is broken.




(2) My meal is cooling because I sprinkled salt on it.




(3) He is good at basketball because he is black.
                                                                            Ex—106

(4) The beach was closed to swimmers because a shark had been sighted earlier in the
    morning.




(5) The candidate changed her view on immigration because she was behind in the
    polls.




(6) The power went out because of the violent storm.
                                                                              Ex—107

Part 2
Read       the        article    at       http://www.washingtonpost.com/wp-
dyn/content/article/2010/02/01/AR2010020102628_pf.html

(7) Make correlation diagrams for each of the four groups (delayed sex, safe sex, both,
    health) in the study.
                                                                                 Ex—108

An Introduction To Reasoning
Exercise Set (1) on 4-Cell Tables (7.4)

For each passage, (i) make a 4-cell table summarizing whatever data is available; (ii) if
possible, calculate the percentage of Fs that are Gs and the percentage of non-Fs that are
Gs; (iii) say whether F and G are correlated, and discuss issues with the sample size and
representativeness.

Sample
   A different study (Kontiokari et al, 2001) sought to evaluate the effects of
   recurrences of UTIs [urinary tract infections] of consuming cranberry-lignonberry
   juice and Lactobacillus GG drink. One hundred and fifty women with UTIs were
   allocated to three treatment groups, one for each juice and a control group. The
   cranberry juice drinkers had 50 ml of cranberry-lingonberry concentrate every day
   for six months. The lactobacillus users had 100 ml of that liquid for five days per
   week over one year. The control group got nothing. "At six months, eight (16%)
   women in the cranberry group, 19 (39%) in the lactobacillus group, and 18 (36%) in
   the     control    group    had     had     at     least  one     recurrence."    (
   http://scienceblogs.com/gregladen/2010/08/does_cranberry_juice_help_repr.php)

   First, we can compare those who got the cranberry juice (present) with the placebo
   (absent):

                                         At Least 1 UTI
                                      Present     Absent             %age
                   Present               8         ~40               16%
       Cranberry
          (Placebo) Absent                18           ~34           36%

   Second, we can compare those who got the lactobacillus with the placebo:

                                         At Least 1 UTI
                                      Present     Absent             %age
                   Present              19         ~30               39%
       Lactobacillus
          (Placebo) Absent                18           ~34           36%

   The results suggest that cranberry juice is negatively correlated with contracting a
   UTI, while lactobacillus does not help.

   The sample sizes are quite small (about 50 in each group) but the study is
   suggestive.

   We do not have any information about sample selection. The fact that there is a
   control group suggests, however, that they were selected randomly.
                                                                              Ex—109

(1) Women who took medication to treat herpes infections during pregnancy weren't
    more likely to have a baby with birth defects than women who didn't take these
    drugs in a study of over 800,000 babies born in Denmark. … During the 12-year
    study, about 1,800 babies were born to mothers who filled prescriptions for
    acyclovir, valacyclovir (Valtrex), and famciclovir (Famvir) during their first
    trimester. Forty of those babies had birth defects - 2.2 percent of them. In
    comparison, close to 20,000 of the 836,000 babies whose mothers didn't take those
    drugs during the first trimester had birth defects, or 2.4 percent. (From
    http://in.reuters.com/article/idINTRE67N5LK20100824)




(2) Children receive several vaccines before age 2, and autism is often diagnosed in 2-
    and       3-year-olds.      Therefore,       vaccinations       cause      autism.
    (http://chronicle.com/article/The-Trouble-With-Intuition/65674/)
                                                                                Ex—110

(3) In a paper published in the Journal of the American Medical Association on Wednesday,
    Ma and colleagues said they tracked for nine years 1,172 diabetes patients in Hong
    Kong who were free of kidney disease at the start of the study. By the end of the
    nine-year study period, 90 of them had developed kidney disease. The researchers
    analysed the DNA of all the participants and found that four mutations of a
    particular gene -- PRKCB1 -- occurred far more frequently in the group with kidney
    disease. "The risk for end-stage renal disease was approximately six times higher for
    patients with 4 risk alleles (mutations) compared with patients with 0 or 1 risk
    allele," they said. (http://www.reuters.com/article/idUSTRE67N5J020100824)




(4) In Cleveland, Tantala reviewed police records for 60,000 traffic accidents taking
    place in the county over an eight-year period, comparing accident rates from a four-
    year period before digital billboards were installed with the four-year period
    following their installation. In Rochester, Tantala reviewed police records
    documenting 18,000 traffic accidents that took place within a mile of digital
    billboards over a five-year period, and in Albuquerque, it reviewed police records
    documenting traffic accidents that took place within a mile of 17 digital billboards
    over a seven-year period. Again, both showed no statistical correlation between
    digital            billboards            and           accidents.              (From
    http://www.mediapost.com/publications/?fa=Articles.showArticle&art_aid=13399
    9)
                                                                                Ex—111



(5) A study of 82 women found that daily text messages didn't help women take their
    birth control pills more consistently — both the text-receiving women and a control
    group missed an average of almost five pills per cycle. (From
    http://blogs.wsj.com/health/2010/08/23/txt-msgs-no-good-4-helping-women-2-
    take-birth-control-pills-study/)




(6) This latest study is a new analysis from a U.S. government-funded clinical trial
    published earlier this year showing no benefit of vitamins C and E in lowering
    preeclampsia risk. For the trial, researchers randomly assigned 10,154 pregnant
    women to take either a combination of vitamins C and E or inactive placebo pills
    beginning somewhere between the 9th and 16th week of pregnancy. All of the
    women had uncomplicated pregnancies and were not at elevated risk of preterm
    delivery. Women in the vitamin group took 1,000 mg of vitamin C and 400 IU of
    vitamin E per day -- much higher than the 85 mg of vitamin C and 22 IU (or about 15
    mg) of vitamin E generally recommended during pregnancy. Overall, 7 percent of
    women in both the vitamin and placebo groups had a preterm birth. (From
    http://www.reuters.com/article/idUSTRE67N4J320100824)
                                                                                 Ex—112

An Introduction To Reasoning
Exercise Set (2) on 4-Cell Tables (7.4)

For each passage, (i) make a 4-cell table summarizing whatever data is available; (ii) if
possible, calculate the percentage of Fs that are Gs and the percentage of non-Fs that are
Gs; (iii) say whether F and G are correlated, and discuss issues with the sample size and
representativeness.

(1) Nearly one in twenty U.S. men have moderate to severe forms of the condition,
    which is as common as one in six among elderly men, a new study finds. Research
    suggests that urinary incontinence affects women about twice as often as it does
    men. But the new findings, researchers say, underscore the fact that despite their
    relatively lower risk, men commonly deal with the condition as well. The study
    found that among 5,300 U.S. men age 20 or older who participated in a government
    health survey, 4.5 percent reported symptoms of moderate to severe urinary
    incontinence -- defined as having leakage at least once a week, or once a month at
    volumes "more than drops." Among men age 75 and older, 16 percent met that
    definition. (http://in.reuters.com/article/idINTRE67M4I220100823)




(2) The actress Jenny McCarthy has used her celebrity to promote proposed cures for
    autism, such as a special diet she designed for her own autistic son. She often talks
    about the thousands of parents who have let her know that her regimen helped their
    children. McCarthy believes, and wants her audience to believe, that those parents
    have    made     a   valid     inference   about    the  effects    of   the    diet.
    (http://chronicle.com/article/The-Trouble-With-Intuition/65674/)
                                                                                 Ex—113

(3) Between July 2008 and March 2009, investigators collected and analyzed fifty
    conventional samples from retail stores in Illinois and Indiana and fifty grass-fed
    samples from 10 sources including retail stores, farm stores, and farmers' markets.
    Around two thirds of the samples in each set were solid cuts of beef (such as steaks)
    while the rest of the samples were ground beef. … The two sample sets had equal
    overall levels of E. coli contamination, at 44 percent. For solid cuts of meat, the
    conventional products had a higher level of E. coli than the grass-fed products, but
    this was reversed for ground beef. Neither difference was significant. (From
    http://www.foodsafetynews.com/2010/08/debate-conventional-v-grass-fed-beef/)




(4) GlaxoSmithKline's diabetes drug Avandia was no riskier to the heart than a rival,
    U.S. researchers said on Tuesday, a finding that contradicts earlier studies and adds
    new fodder to the roiling debate over the drug's safety. The study of more than
    36,000 diabetics, done by researchers at health insurer WellPoint Inc, found the risks
    of death or having a heart attack, heart failure or both were the same, about 4
    percent, for patients taking either Avandia, known generically as rosiglitazone, or
    Takeda Pharmaceutical Co's Actos, known generically as pioglitazone. (From
    http://www.reuters.com/article/idUSTRE67N5XR20100824)
                                                                               Ex—114

(5) A study which was recently completed by Mulley Communications found that
    Facebook users spend more time looking at advertisements on profile pages than on
    the homepage. … 71% of users looked at adverts on their Profile pages, 31% of users
    looked at adverts on the News Feed page (homepage).! Users pay more attention
    (53% vs. 31%) to page updates in their News Feed Wall rather than adverts to the
    right-hand side of the Wall. 30 out of the 40 users log on to Facebook once a day or
    more. (From http://www.allfacebook.com/study-facebook-profile-ads-are-more-
    effective-than-homepage-ads-2010-07)
                                                                                    Ex—115

An Introduction To Reasoning
Exercise Set (1) on Evaluating Explanations (7.5)

For each passage, (i) say whether or not the explainee is not correlated with, correlated
but caused by, or, both correlated with and caused by, the explainer. (ii) Explain your
answer; include a discussion of the strength of the correlation and whether the
explanation is satisfying.

Sample
     Gill passed her History exam because she is very smart.

       Being very smart is correlated with passing exams (History or otherwise), and is
       a cause of Gill's success. But a more satisfying explanation would appeal to more
       specific factors about Gill and her exam, for example, that she studied a lot for it,
       or that she had already covered the material elsewhere.


(1) These crackers are stale because they are past their sell-by date.




(2) I was late to class because traffic was terrible. It was terrible because Main Street was
    closed for road repairs.
                                                                               Ex—116

(3) Henry is speaking: I trust Bill about car repair because he worked for 6 years as a
    mechanic, during his high-school and college years.




(4) Jack has a cold because he took a walk right after he washed his hair, on a freezing
    cold day.




(5) There is wind because the trees move back and forth.
                                                                                Ex—117

(6) Adopting a child helps couples who are having difficulties to conceive a child of
    their own.




(7) Movie theatres see an increase in customers during (and because of) recessions.




(8) Jim Furyk was disqualified from the golf tournament because he arrived late and
    missed his tee-time. He missed his tee-time because the battery of his mobile phone,
    which he was using for an alarm, ran out.
                                                                                Ex—118

An Introduction To Reasoning
Exercise Set (2) on Evaluating Explanations (7.5)

For each passage, (i) say whether or not the explainee is not correlated with, correlated
but caused by, or, both correlated with and caused by, the explainer. (ii) Explain your
answer; include a discussion of the strength of the correlation and whether the
explanation is satisfying.

(1) Christopher Hitchens got cancer because he does not believe in the Christian god.




(2) The Irish are happy because they always think about how things could always be
    worse.




(3) Adding salt (at the table) causes food to cool.
                                                            Ex—119

(4) The airplane crashed because ice formed on the wings.




(5) Plants grow because they receive sunlight.




(6) Divorce is caused by marriage.
                                                                             Ex—120

(7) School shootings happen because kids play violent video games.




(8) Mobile phones and texting are making young people increasingly unable to focus.




(9) Marriage causes women to get pregnant.
                                                                                 Ex—121

An Introduction To Reasoning
Exercise Set (1) on Necessary and Sufficient Conditions, INUS Conditions (8.1-2)

Part I. Good definitions provide necessary and sufficient conditions. For each of the
following suggested definitions, say whether or not the definition on offer provides (i) a
necessary condition, (ii) a sufficient condition, for what is being defined, and, (iii) in
each case where you give a negative answer, provide a counter-example as an
illustration.

Sample

Chair: a four-legged seat.
Necessary Condition:       Yes         No
       Counterexample: A wheelchair (is a chair but has no legs).

Sufficient Condition:    Yes           No
       Counterexample: A couch (is a four-legged seat but not a chair).


(1) Human: a tool-using animal.
Necessary Condition:      Yes            No
      Counterexample:


Sufficient Condition:      Yes           No
       Counterexample:



(2) Person who has successfully completed undergraduate studies at this institution:
    someone who has taken and passed at least 32 classes.
Necessary Condition:     Yes          No
       Counterexample:


Sufficient Condition:      Yes           No
       Counterexample:



(3) (A) Painting: a design drawn on canvas with a brush.
Necessary Condition:        Yes         No
       Counterexample:


Sufficient Condition:      Yes           No
       Counterexample:
                                                                                     Ex—122



(4) (A) Parent: one's immediate biological ancestor.
Necessary Condition:       Yes           No
       Counterexample:


Sufficient Condition:        Yes           No
       Counterexample:


Part 2.
For each item listed, (i) Give a (single) INUS condition; (ii) spell out some of the other
factors that go along with (i) in order to form a jointly sufficient condition for the effect;
(iii) explain why it (the joint condition in (ii)) is not necessary by giving another
(individually or jointly) sufficient cause.

(5) An individual becomes President/Prime Minister of [the country you are in].




(6) An elected official resigns.




(7) The water in a heated pot evaporates and the bottom of the pot burns.




(8) The power goes out.
                                                                                   Ex—123

An Introduction To Reasoning
Exercise Set (2) on Necessary and Sufficient Conditions, INUS Conditions (8.1-2)

Part I. Good definitions provide necessary and sufficient conditions. For each of the
following suggested definitions, say whether or not the definition on offer provides (i) a
necessary condition, (ii) a sufficient condition, for what is being defined, and, (iii) in
each case where you give a negative answer, provide a counter-example as an
illustration.

(1) Wolverine: not a bear and not a wolf. (note: the animal, not the fictional character)
Necessary Condition:       Yes           No
      Counterexample:


Sufficient Condition:       Yes           No
       Counterexample:



(2) Kitchen: a room in a house in which food is prepared and cooked
Necessary Condition:       Yes          No
       Counterexample:


Sufficient Condition:       Yes           No
       Counterexample:



(3) Painting: applying color to a surface.
Necessary Condition:       Yes             No
       Counterexample:


Sufficient Condition:       Yes           No
       Counterexample:



(4) Salt: NaCl
Necessary Condition:        Yes           No
       Counterexample:


Sufficient Condition:       Yes           No
       Counterexample:
                                                                                     Ex—124

Part 2.
For each item listed, (i) Give a (single) INUS condition; (ii) spell out some of the other
factors that go along with (i) in order to form a jointly sufficient condition for the effect;
(iii) explain why it (the joint condition in (ii)) is not necessary by giving another
(individually or jointly) sufficient cause.


(5) No one's mobile phone rings in class.




(6) A human being becomes drunk.




(7) A student fails to do his/her homework.




(8) The rate of motor accidents increases from one year to the next.




(9) A car refuses to start.
                                                                              Ex—125

Part 3

(10) Make a list of all of the explanatory factors (for the candidates' success)
    mentioned in this article
    http://www.miamiherald.com/2010/08/22/1786600/mccollum-meek-surge-
    ahead-of-rivals.html .
                                                                                 Ex—126

An Introduction To Reasoning
Exercise (1) on Experimental Methods (8.3-6)

(1)   Read the following paragraph and describe in your own words how Mangan
      isolated soil as the cause:

      Scott Mangan -- of the University of Wisconsin, Milwaukee, and the Smithsonian
      Tropical Research Institute in Panama -- has succeeded to isolate soil as the cause
      [of the lower survival rates of seedlings growing near trees of the same species]
      with a clever experiment conducted in parallel in the native environment and the
      greenhouse. Mangan planted five species of seedlings in the forest and also
      collected dirt nearby for growing seedlings in a greenhouse in soils that match the
      soil of the trees planted in nature. The similarity of the results in the greenhouse
      and results in the natural environment provide strong evidence that the relevant
      enemies are in the soil. (treehugger.com)




(2)   In a study of chimpanzee altruism (helping others without being rewarded for it)
      "a Leipzig team reported that chimps would help their human keepers retrieve a
      pen that they had dropped — an action with no direct benefit for the chimp." What
      might explain this behavior, other than altruism? How might you change this
      experiment in order to test for your worries? (nature.com)
                                                                                 Ex—127

(3)   One explanation of the results cited below is that god(s) does not exist. Come up
      with alternative explanations.
      After three years, $2.4 million, and 1.7 million prayers, the biggest and best study
      ever was supposed to show that the prayers of faraway strangers help patients
      recover after heart surgery. But things didn't go as ordained. Patients who
      knowingly received prayers developed more post-surgery complications than did
      patients who unknowingly received prayers—and patients who were prayed for
      did no better than patients who weren't prayed for. In fact, patients who received
      prayers without their knowledge ended up with more major complications than
      did patients who received no prayers at all. (slate.com)




(4)   Describe the manipulation used in the following experiment and say what you
      think the experiment shows.
      A study conducted in 1999 by Read, Loewenstein and Kalyanaraman had people
      pick three movies out of a selection of 24. Some were lowbrow like "Sleepless in
      Seattle" or "Mrs. Doubtfire." Some were highbrow like "Schindler's List" or "The
      Piano." … After picking, the subjects had to watch one movie right away. They
      then had to watch another in two days and a third two days after that.
               Most people picked Schindler's List as one of their three. … When they
      ran the experiment again but told subjects they had to watch all three selections
      back-to-back, "Schindler’s List" was 13 times less likely to be chosen at all.
      (youarenotsosmart.com)
                                                                           Ex—128

An Introduction To Reasoning
Exercise (2) on Experimental Methods (8.3-6)

(1)   Read the abstract and comment at http://www.iqscorner.com/2006/05/dyslexia-
      and-eye-tracking-problems.html and describe in your own words how the
      experiment was found to support only one of the two prevailing hypotheses.




(2)   Read       the       article    "Anaesthetics      damage       the fetus" at
      http://books.google.co.uk/books?id=DilcKbMBXRMC&lpg=PA577&dq=anaesthe
      tics damage the fetus&pg=PA577 - v=onepage&q=anaesthetics damage the
      fetus&f=false and describe in your own words how the experiment was able to
      isolate the effect of laughing gas from the alternative hypotheses.
                                                                             Ex—129

(3)   Watch the video at http://www.youtube.com/watch?v=nUdsTizSxSI and
      describe in your own words any one experiment which changes a variable in order
      to test an effect.




(4)   Read the article at http://www.slate.com/id/2131645/ and describe in your own
      words how Miller pursued her hypothesis and why, at each stage, she chose to
      compare the groups she did.
                                                                               Ex—130

(5)   Read the article at http://www.latimes.com/health/boostershots/la-heb-
      pregnancy-20100804,0,3195262.story.
      What are the two competing explanations for larger babies, mentioned at the top of
      the article? Which do the researchers cited in the article prefer, and why?




(6)   Watch the video at http://www.ehow.com/video_4997786_power-door-lock-
      troubleshooting.html and make a list of the possible causes and the tests one
      should do in order to work out why the power door locks (on a car) do not work.
                                                                                         Ex—131

An Introduction To Reasoning
Exercise Set (1) on Arguments Involving Explanations (9.1-5)

For each argument, (i) put the argument in standard form, including (as missing
premises, if necessary) the "additional" premises needed to make the argument cogent;
(ii) underline "IE" if it is an instance of inference to an explainee, underline "ML" if it is
an instance of inference to the most likely explanation, and underline "AAn" if it is an
instance of argument from analogy, (iii) discuss whether the "additional" premises are
true; (iv) underline "Sound" if the argument is sound, and "Unsound" if the argument is
unsound and (v) explain your choice.

Sample

    I [Jack] drove home yesterday and as I was slowing down on our street, I heard a
    clip-clop sound. It might have been some kid knocking two coconut halves together,
    but the most likely explanation is probably a police officer on horse-back. So, that's
    probably what I heard.

        IE       ML                AAn                                       Sound   Unsound

(1) A clip-clop sound is.
(2) An officer on horse-back is an explanation for (1).
(3) The explanation in (2) is the most likely explanation.
    ----------------------------------------------------------------------
(4) An officer was riding by on a horse.

Discussion: Jack's candidate explainer is rather specific: an officer was on horse-back. He
   could have simple said a person was riding a horse. I suspect he is drawing on past
   experience (of officers patrolling on horse-back in his neighborhood and no other
   horse-riders). So, I am willing to accept the argument.

(1) In all likelihood, there's smoke coming from the chimney. For I can see clearly that
    there's a fire in the fireplace, and fires in fireplaces explain smoke's coming from a
    chimney.

        IE       ML                AAn                                       Sound   Unsound
                                                                                  Ex—132

(2) TVs are being designed to use thin-film interference, and because cephalopod skin
    uses thin-film interference to generate color, that implies that cephalopod skin is
    also designed.

      IE     ML            AAn                                Sound         Unsound




(3) In the bar last night, Henry struck the match at midnight. This potentially explains
    the match’s lighting just after midnight, in that if a person were to strike a match at
    midnight (in normal conditions), it would light just after midnight. Thus, there is
    good reason for thinking that the match lit just after midnight.

      IE     ML            AAn                                Sound         Unsound
                                                                               Ex—133

(4) When the temperature of the air rises, ice around the global caps melts and the seas
    rise. The air temperature will rise gradually but significantly over the next fifty
    years. So, the sea-level of the oceans will rise over the next fifty years.

      IE     ML            AAn                              Sound         Unsound




(5) The patient has a large red circular rash. This type of rash is a symptom of Lyme
    disease. So, the patient probably has Lyme disease.

      IE     ML            AAn                              Sound         Unsound
                                                                                  Ex—134

(6) Most times when it rains heavily, it causes the garden to flood. Since we're
    experiencing a real downpour at the moment, it's likely that the garden will flood.

      IE     ML            AAn                                Sound         Unsound




(7) Consider the underlined argument in the following scenario: Jack has had a tooth filled
    without an anesthetic. Gill reasons that it must have been painful, as follows: "When
    humans have a tooth filled without an anaesthetic, it hurts. Jack is a human, with a
    regular nervous system as anyone else. I infer that Jack felt considerable pain in his
    situation.".

      IE     ML            AAn                                Sound         Unsound
                                                                              Ex—135

(8) This woman is producing milk. Women who produce milk are nursing mothers or
    are about to give birth. So, this woman is a nursing mother or about to give birth.

      IE     ML           AAn                               Sound        Unsound




(9) Toyota is known for its quality engines and careful manufacturing process, and
    these are responsible for the durability of Toyota vehicles. Jack's new truck is a
    Toyota with a Toyota engine and manufacture. So, Jack's new truck will be durable.

      IE     ML           AAn                               Sound        Unsound
                                                                                       Ex—136

An Introduction To Reasoning
Exercise Set (2) on Arguments Involving Explanations (9.1-5)

For each argument, (i) put the argument in standard form, including (as missing
premises, if necessary) the "additional" premises needed to make the argument cogent;
(ii) underline "IE" if it is an instance of inference to an explainee, underline "IBAE" if it is
an instance of inference to the best available explanation, and underline "AAn" if it is an
instance of argument from analogy, (iii) discuss whether the "additional" premises are
true; (iv) underline "Sound" if the argument is sound, and "Unsound" if the argument is
unsound; (v) if the argument is incogent, explain why.

(1) The docks of three other abandoned houses in the area are made of old wood, they
    creak, and the nails are rusty. It's no surprise that the three docks have collapsed in
    various places, since these kinds of wear lead to collapse. The dock of this house we
    are at is also made of old wood, is creaking, and has rusty nails. It will likely
    collapse.

       IE     ML             AAn                                  Sound          Unsound




(2) Brian has dreads and wears lots of funky clothes. Adam is Brian's friend, and like
    Brian he has dreads and wears lots of bright colors. They both work at the same
    restaurant. Adam smokes weed. So, my guess is that Brian smokes weed, too.

       IE     ML             AAn                                  Sound          Unsound
                                                                                   Ex—137

(3) The President is about to sign new "green" tax cuts into law. A result of these cuts
    will be an increase in investment in renewable fuels. So, such investment will
    increase.

       IE     ML            AAn                                Sound         Unsound




(4) Consider the underlined portions of the following: Your lights are on, but you're not
    home. Your mind is not your own. Your heart sweats, your body shakes. Another
    kiss is what it takes. You can't sleep, you can't eat. There's no doubt, you're in deep.
    Your throat is tight, you can't breathe. Another kiss is all you need. Whoa. You like
    to think that you're immune to the stuff, oh yeah. It's closer to the truth to say you
    can't get enough. You know you're gonna have to face it: you're addicted to love.
    (Robert Palmer, 'Addicted to Love', Riptide, 1985)

       IE     ML            AAn                                Sound         Unsound
                                                                                Ex—138

(5) Lori auditioned at 17. The best explanation for this is that she started dancing at a
    very young age. So, Lori probably started dancing at an early age.

      IE     ML            AAn                               Sound         Unsound




(6) Riding a horse requires the same kind of balance as sitting on a (surf) board does.
    They're both about 20 inches wide, you sit in the middle and put your legs over the
    side.

      IE     ML            AAn                               Sound         Unsound
                                                                                  Ex—139

(7) Geez, this Obama guy inserts so many complications and qualifications in what he
    says. He's like a back-country road with so many twists and turns that no one ever
    uses it. My guess is that no one is following him now.

       IE     ML            AAn                                Sound         Unsound




(8) Gill's roses are in moderately heavy clay soil, have natural rainfall as their only
    source of water, and are free of disease. Jack's roses, just like Gill's, will be in
    moderately heavy clay soil, and will have natural rainfall as their only source of
    water. Since these are the main features relevant to growing plants, in all probability
    Jack's roses, just like his neighbor Gill's, will be free of disease.

       IE     ML            AAn                                Sound         Unsound
                                                                               Ex—140

(9) The New York City medical examiner, Dr Charles Norris himself, was on call the
    night of the Travia arrest. … The blood pooled around the half-body was a bright
    cherry-red. He bent to look closer at the woman's face. It was flushed pink, despite
    the massive blood loss. … Norris's reaction to the corpse came from a simple fact:
    people killed by the poisonous gas carbon monoxide tend to flush pink, the result of
    a chemical reaction in the blood. A murder victim who bleeds to death would have
    been porcelain pale. ... Their dismembered corpse had been dead before Travia
    picked up the knife. (From The Poisoner's Handbook, Deborah Blum)

      IE     ML            AAn                              Sound         Unsound
                                                                          Ex—141

An Introduction To Reasoning
Exercise Set (1) on Categorical Logic (10.5)

Part 1
(1) Consider the following proposition:

       Some politicians are not members of tennis clubs.

   (a) Make a translation key for it.




   (b) Construct a Venn diagram for the information in the proposition.




(2) Consider the following proposition:

       No dog has ever been to Mars.

   (a) Make a translation key for it.




   (b) Construct a Venn diagram for the information in the proposition.
                                                                            Ex—142

Part 2
(3) Consider the following argument:

      No one who likes the Yankees likes the Red Sox. Thus, anyone who likes the Red
      Sox doesn't like the Yankees.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                                   Ex—143

(4) Consider the following argument:

      All the boxes in the attic are old and musty. Moreover, some pieces of furniture
      are old and musty. So necessarily, all the boxes in the attic are pieces of furniture.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                           Ex—144

(5) Consider the following argument:

      All spiders make thread, and anything that makes thread makes webs. So for
      sure, all spiders make webs.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                               Ex—145

(6) Consider the following argument:

      Some children are not afraid to explore. For no one afraid to explore suffers from
      abandonment issues, and some children suffer from abandonment issues.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                              Ex—146

(7) Consider the following argument:

      Every professional baseball player is a professional athlete, and no professional
      athlete is poor. No professional baseball player, thus, is poor.


   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                           Ex—147

(8) Consider the following argument:

      No horse contracts scrapie. So, because some animals contracting scrapie lose
      weight, there are horses that do not lose weight.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                          Ex—148

An Introduction To Reasoning
Exercise Set (2) on Categorical Logic (10.5)

Part 1

(1) Consider the following proposition:

         Every dog loves hot dogs.

   (a) Make a translation key for it.




   (b) Construct a Venn diagram for the information in the proposition.




(2) Consider the following proposition:

         Some dog owners are cruel.

   (a) Make a translation key for it.




   (b) Construct a Venn diagram for the information in the proposition.
                                                                           Ex—149

Part 2
(3) Consider the following argument:

      All actors are fakers. Some fakers, therefore, are actors.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                                Ex—150

(4) Consider the following argument:

      Since everyone in this room is enrolled in logic, and since everyone at the college
      is enrolled in logic, everyone in this room is attending the college.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                           Ex—151

(5) Consider the following argument:

      All arguments are attempts to convince, and some attempts to convince are
      denials of autonomy. Therefore, some arguments are denials of autonomy.



   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                           Ex—152

(6) Consider the following argument:

      No one who likes smoked eel are completely reliable. For, everyone who likes
      smoked eel is a person with odd characteristics, and no one with odd
      characteristics is completely reliable.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                               Ex—153

(7) Consider the following argument:

      Breaking an addiction requires self-control, and nothing requiring self-control is
      easy. Thus, breaking an addiction is never easy.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                           Ex—154

(8) Consider the following argument:

      Jack is an American soldier in Iraq, and some American soldiers in Iraq are
      unable to sleep much. Hence, Jack is unable to sleep much.

   (a) Make a translation key for it.




   (b) Relative to the key, put it in standard form.




   (c) Relative to what you have in standard form, construct a Venn diagram for the
   information in the premises.




   (d) Relative to your diagram and what you have in standard form, is the argument
   valid?
                                                                             Ex—155

An Introduction To Reasoning
Exercise Set (1) on Logically Structured English (11.2-4)

For each assertion, use the translation key below to put the assertion into Logically
Structured English. Use brackets as necessary.

     b: Jack is a bachelor
     f: Jack has all ten fingers
     g: Gill will go out with Jack
     l: Jack likes orange juice
     m: Jack is married
     s: Jack says that he is a bachelor

(1) Jack is a bachelor and likes orange juice.




(2) Jack is a bachelor, and he says he's a bachelor.




(3) Jack is not married, and Gill will go out with Jack.




(4) If Jack is unmarried, Gill will go out with him.




(5) Although Jack isn't married, Gill will not go out with him.
                                                                                      Ex—156

(6) Jack is not both married and ten-fingered.




(7) It's not the case that Jack either likes orange juice or has all ten fingers.




(8) If Jack has ten fingers or likes orange juice, then, if he is a bachelor, then Gill will go
    out with him.
                                                                                      Ex—157

An Introduction To Reasoning
Exercise Set (2) on Logically Structured English (11.2-4)

For each assertion, use the translation key below to put the assertion into Logically
Structured English. Use brackets as necessary.

b: Jack is a bachelor
f: Jack has all ten fingers
g: Gill will go out with Jack
l: Jack likes orange juice
m: Jack is married
s: Jack says that he is a bachelor

(1) Jack is either married or a bachelor.




(2) Jack is married, but says he's a bachelor.




(3) Jack neither is a bachelor nor says he's a bachelor.




(4) Jack is unmarried if he's a bachelor.




(5) If Jack likes orange juice and says he's a bachelor, Gill will go out with him.
                                                                                   Ex—158

(6) Jack has all ten fingers.




(7) Jack isn't married, yet he's not a bachelor.




(8) Either Jack is married or he’s not, and either Gill will go out with him or she won't.
                                                                                    Ex—159

An Introduction To Reasoning
Exercise (1) on Logically Structured English (11.2-3, 11.5)

For each proposition, use the translation key below to put the assertion into Logically
Structured English. Use parentheses as necessary.

    b: Jack is a bachelor
    f: Jack has all ten fingers
    g: Gill will go out with Jack
    l: Jack likes orange juice
    m: Jack is married
    s: Jack says that he is a bachelor

(1) Gill will go out with Jack if he likes orange juice.




(2) A sufficient condition for Gill's going out with Jack is that he's unmarried.




(3) It's not the case that if Jack says he's a bachelor then he is a bachelor.




(4) Unless Jack says he's a bachelor, Gill will not go out with him.




(5) Even though Jack is not in fact a bachelor, Gill will go out with him provided that
    both he says he's a bachelor and he likes orange juice.
                                                                              Ex—160

(6) Jack isn't a bachelor unless he isn't married.




(7) Jack's being unmarried is not a necessary condition for Gill's going out with him,
    however it is necessary that he has all ten fingers.




(8) Only if Jack is a bachelor will Gill go out with him.
                                                                                    Ex—161

An Introduction To Reasoning
Exercise (2) on Logically Structured English (11.2-3, 11.5)

For each proposition, use the translation key below to put the assertion into Logically
Structured English. Use parentheses as necessary.

    b: Jack is a bachelor
    f: Jack has all ten fingers
    g: Gill will go out with Jack
    l: Jack likes orange juice
    m: Jack is married
    s: Jack says that he is a bachelor

(1) Jack's not being married is necessary for Gill to go out with him.




(2) Gill will go out with Jack only if Jack is both a bachelor and likes orange juice.




(3) Jack's having all ten fingers, together with his liking orange juice, is sufficient for
    Gill's going out with him.




(4) Gill will go out with Jack if and only if he's a ten-fingered bachelor.




(5) Provided that Jack says he's a bachelor, Gill will go out with him.
                                                                                    Ex—162



(6) Jack is a bachelor only if Jack is unmarried; but, of course, it's false that Jack is a
    bachelor if Jack is unmarried.




(7) Only if Jack is a bachelor and either likes orange juice or has all ten fingers will Gill
    go out with him.
                                                                                 Ex—163

An Introduction To Reasoning
Exercise Set (1) on 4 of the Big 8 (11.6-9)

For each argument (i) make a translation key for each simple proposition, (ii) relative to
the key, put the argument in standard form using logically structured English, (iii)
relative to what you have in standard form, say whether the argument an instance of
AA, AC, CC or CA, (iv) relative to your answer to (iii), say whether or not it is valid.

Sample

   The fan will run only if the light is switched on. The light is not switched on.
   Therefore, the fan will not run.

   r = The fan will run.                               (1) If r then s.
   s = The light is switched on.                       (2) not s
                                                           --------------
                                                       (3) not r

       AA     AC      CC     CA                                Valid        Not valid


(1) If watching TV is genuinely relaxing, it enhances the quality of life. But since
    watching TV isn't genuinely relaxing, it doesn't enhance the quality of life.




       AA     AC      CC     CA                                Valid        Not valid


(2) Clearly, Jack isn't nervous. After all, if Jack is between Gill and Henry then he's
    nervous, and he isn't between Gill and Henry.




       AA     AC      CC     CA                                Valid        Not valid
                                                                                Ex—164

(3) Provided that Smith is not beaten by more than 10 points in Ohio, Smith will win the
    nomination. But Smith will not win the nomination. So, he will be beaten by more
    than 10 points in Ohio.




      AA     AC     CC     CA                                Valid         Not valid



(4) Coherentism is not false, since sensory experiences can serve as good reasons only if
    coherentism is false, and since sensory experiences can't serve as good reasons.




      AA     AC     CC     CA                                Valid         Not valid


(5) We don't have both a leash and a pooper-scooper for Jim. Unless we have both, he
    can't go to the park. So, Jim can't go to the park.




      AA     AC     CC     CA                                Valid         Not valid
                                                                                 Ex—165

An Introduction To Reasoning
Exercise Set (2) on 4 of the Big 8 (11.6-9)

For each argument (i) make a translation key for each simple proposition, (ii) relative to
the key, put the argument in standard form using logically structured English, (iii)
relative to what you have in standard form, say whether the argument an instance of
AA, AC, CC or CA, (iv) relative to your answer to (iii), say whether or not it is valid.

(1) Jack will come camping this weekend provided that either Smith or Jones also come.
    However, both Smith and Jones cannot go this weekend. So, Jack won't be coming
    either.




       AA     AC      CC     CA                               Valid         Not valid


(2) Only if the pool boy removed all the leaves, will he get paid. Hence, since he
    removed all the leaves, he'll get his money.




       AA     AC      CC     CA                               Valid         Not valid
                                                                                   Ex—166



(3) Life isn't always better than death. For if life is always better than death then no one
    commits suicide, and, of course, it's not the case that no one commits suicide.




       AA     AC     CC     CA                                 Valid         Not valid

(4) Henry will graduate this June only if he passes Introduction to Formal Logic this
    term. He won't graduate this June. Hence, he won't pass Introduction to Formal
    Logic this term.




       AA     AC     CC     CA                                 Valid         Not valid

(5) If Smith can raise a lot more money and gain the support of the unions, he will win
    the nomination and become President. But Smith won't win the nomination and
    become President. So, he won't raise a lot more money and gain the support of the
    unions.




       AA     AC     CC     CA                                 Valid         Not valid
                                                                                  Ex—167

An Introduction To Reasoning
Exercise Set (1) on the Big 8 (11.10)

For each argument (i) make a translation key, (ii) relative to the key, put the argument
in standard form using logically structured English, (iii) relative to what you have in
standard form, say whether the argument an instance of AA, AC, CC, CA, HS, DS, CD
or DD, (iv) relative to your answer to (iii), say whether or not it is valid.

Sample

   Either wealth increases subjective well-being, or it is not the case that money can
   buy happiness. Given this and given that it is not the case that wealth increases
   subjective well-being, it is not the case that money can buy happiness.

   i = Wealth increases subjective well-being.
   b = Money can buy happiness.

   1. i or not b
   2. not i
      -------------
   3. not b

       AA       AC    CC     CA     HS   DS      CD    DD            Valid Not valid

(1) If atheists can be moral, then there is no need for gods. Further, all our good works
    are in vain if there is no need for gods. We can conclude with certainty thus, that all
    our good works are in vain provided that atheists can be moral.




       AA       AC    CC     CA     HS   DS      CD    DD            Valid Not valid
                                                                                       Ex—168

(2) Teenage pregnancy can be reduced only if the schools dispense birth control to
    students. But if they dispense birth control, they encourage underage sex. So,
    schools will encourage underage sex if they reduce teenage pregnancies.




       AA     AC      CC     CA     HS      DS     CD      DD            Valid Not valid

(3) If what the Congressional Report says is true, then there never were any WMDs in
    Iraq and the war was poorly motivated. If the President is telling the truth, on the
    other hand, Iraq has a complete nuclear weapons program. So, because one of them
    is right, we can conclude with certainty that either there never were any WMDs in
    Iraq and the war was poorly motivated, or Iraq has a complete nuclear weapons
    program.




       AA     AC      CC     CA     HS      DS     CD      DD            Valid Not valid


(4) Jim's being a dog is sufficient for Jim's being an animal, and Jim's being an animal is
    sufficient for Jim's not being a television. Jim's being a dog, therefore, is sufficient for
    Jim's not being a television.




       AA     AC      CC     CA     HS      DS     CD      DD            Valid Not valid
                                                                                    Ex—169

(5) If Jim can't go to the park, he will not be able to chase squirrels or catch the frisbee.
    If, on the other hand, he does go to the park, he will miss barking at the mailman.
    But of course, Jim either will go to the park or he won't. Hence, either he will not be
    able to chase squirrels or catch the frisbee, or he will miss barking at the mailman




       AA     AC     CC     CA     HS     DS      CD     DD            Valid Not valid
                                                                                    Ex—170

An Introduction To Reasoning
Exercise Set (2) on the Big 8 (11.10)

For each argument (i) make a translation key, (ii) relative to the key, put the argument
in standard form using logically structured English, (iii) relative to what you have in
standard form, say whether the argument an instance of AA, AC, CC, CA, HS, DS, CD
or DD, (iv) relative to your answer to (iii), say whether or not it is valid.


(1) Either no actions are free or some events don't have a cause. Given this and given
    that it's not the case that no actions are free, it follows with certainty that some
    events don't have a cause.




       AA     AC     CC      CA     HS    DS      CD     DD            Valid Not valid

(2) If an argument is good, it is logically correct, since if an argument is good it is sound
    and if an argument is sound it is logically correct.




       AA     AC     CC      CA     HS    DS      CD     DD            Valid Not valid
                                                                                   Ex—171



(3) State will go to the Rose Bowl provided that it wins against Tech this week. It'll go to
    the Sugar Bowl if it loses to Tech this week. And, of course, either it'll win or lose
    against Tech. So necessarily, it'll go to either the Rose Bowl or the Sugar Bowl.




       AA     AC     CC     CA     HS     DS     CD     DD            Valid Not valid

(4) If Gill stays in tonight, she'll get up tomorrow morning at six. If she doesn't stay in
    tonight, she won't get up tomorrow morning until nine. Thus, given that she'll either
    stay in tonight or not, she'll either get up tomorrow morning at six or not get up
    until nine.




       AA     AC     CC     CA     HS     DS     CD     DD            Valid Not valid

(5) Either the Marlins and the Raiders lose, or the Bears make the play-offs. Since the
    Bears did not make the play-offs, it's not the case that the Marlins and Raiders both
    lost.




       AA     AC     CC     CA     HS     DS     CD     DD            Valid Not valid
                                                                              Ex—172

An Introduction To Reasoning
Exercise Set (1) on Logically Structured Symbolic Propositions (12.2)

Part 1
For each proposition, underline "Yes" if it is well-formed and "No" if it is not well-
formed.

(1) ~bc ⊃ b

   Yes       No

(2) g & (h ∨ ~i ⊃ j)

   Yes       No

(3) t & ~r

   Yes       No

(4) t & ∨ r

   Yes       No

Part 2
For each proposition, use the translation key provided and put the assertion into
symbolic. Use parentheses appropriately.

       b: Jack is a bachelor.
       f: Jack has all ten fingers.
       g: Gill will go out with Jack
       l: Jack likes orange juice.
       m: Jack is married
       s: Jack says that he is a bachelor.

(5) Either Jack is a bachelor, or he's married and says he's a bachelor.




(6) If Jack is unmarried, then he's a bachelor and he says he's a bachelor.
                                                                                   Ex—173

(7) Gill will go out with Jack provided that he is a bachelor and he doesn't like orange
    juice.




(8) It's not the case that Jack both likes orange juice and has all ten fingers.




Part 3
For each assertion, make a translation key and translate it into symbolic.

(9) The Marlins will win the World Series this year if, both, the Yankees won't win it
    this year and some team will win it this year.




(10) Either the Yankees will win Game 2 and George will be happy, or they won't win
    and George won't be happy.




(11)   If either Bob or Alice come camping, Xena will too.
                                                                                    Ex—174

An Introduction To Reasoning
Exercise Set (2) on Logically Structured Symbolic Propositions (12.2)

Part 1
For each assertion, underline "Yes" if it is well-formed and "No" if it is not well-formed.

(1) ~((m ∨ ~~n) ⊃ (j & m)

    Yes    No

(2) b & c & d

    Yes    No

(3) (B ∨ c) ⊃ d

    Yes    No

(4) ~((f & g) ∨ r)

    Yes    No

Part 2
For each proposition, use the translation key provided and put the assertion into
symbolic. Use parentheses appropriately.

       b: Jack is a bachelor.
       f: Jack has all ten fingers.
       g: Gill will go out with Jack
       l: Jack likes orange juice.
       m: Jack is married
       s: Jack says that he is a bachelor.

(5) Jack is married, and although he says he is a bachelor, he is not a bachelor.




(6) Either Jack is married or he's not, and either Gill will go out with him or she won't.
                                                                                 Ex—175

(7) If Jack likes orange juice, Gill will go out with him, and if he is a bachelor he is
    unmarried.




(8) It's not the case that Jack is unmarried.




Part 3
For each assertion, make a translation key and translate it into symbolic.

(9) Although the Yankees had the home-field advantage in Game 1, the Marlins won 3-
    2.




(10)   The crops will fail and the well will run dry unless it rains tomorrow.




(11) The match being dry and the presence of oxygen are necessary conditions for
    lighting the match.
                                                                                  Ex—176

An Introduction To Reasoning
Exercise Set (1) on the Method of Derivation (6 Rules) (12.4)

For each argument, give a translation key and show that the following arguments are
valid by the method of derivation (writing the propositions in symbolic ⊃ ∨), using only
the basic six rules.

Sample

      Jim can go to the park only if we have a pooper-scooper. We don't have a pooper-
      scooper. So, no park for Jim.

g = Jim can go to the park.
p = We have a pooper-scooper.

       1. g ⊃ p             Premise
       2. ~p                Premise                                   Conclusion: ~g
       3. ~g                1, 2 CC


(1)   If a dog is foaming at the mouth, it has rabies. If it has rabies, it needs to be put
      down. So, if a dog is foaming at the mouth, it needs to be put down.




(2)   If we (the USA) want to see an improvement in college graduation rates—and we
      certainly do—we should increase funding at the kindergarten level. So, that's what
      we should do.
                                                                                  Ex—177

(3)   If this solution can neutralize bases, it can be used to remove cuticles. But this
      solution does not remove cuticles. If the solution is acidic it can neutralize bases.
      What's more, if the litmus paper will turn red then the solution is acidic. So, the
      litmus paper will not turn red.




(4)   There are trails of slime going toward the bed of peas only if there are slugs in the
      bed of peas. On the other hand, if there are holes in the peas then there are aphids
      in your bed of peas. But either there are no aphids or no slugs. So, there are either
      no slime trails or no holes. And there are indeed holes, so there are no trails of
      slime.
                                                                                    Ex—178

An Introduction To Reasoning
Exercise Set (2) on the Method of Derivation (6 Rules) (12.4)

For each argument, give a translation key and show that the following arguments are
valid by the method of derivation (writing the propositions in symbolic), using only the
basic six rules.

(1) You don't have a GPA of greater than 2.0. Having a GPA higher than 2.0 is a
    necessary condition for graduation. So, you cannot graduate.




(2) If Jack is a bachelor, then, if he likes orange juice, Gill will go out with him. He is a
    bachelor. He likes orange juice. So, Gill will go out with him.




(3) If Tech wins the game on Saturday, State will not make the conference play-offs. If
    Tech does not win the game on Saturday, either their coach will be fired or their
    quarterback will be replaced. But there's no way State will not make the play-offs.
    And, there's no way the coach will be fired. So, the quarterback will be replaced.
                                                                                 Ex—179

(4) If too many people withdraw from the market, confidence will plummet. If
    confidence plummets, investment will dry up. If investment dried up,
    unemployment will increase. And if unemployment increases, people will stop
    spending. So, if too many people withdraw from the market, people will stop
    spending.




(5) The train is covered in a half inch of snow. If the train is covered in a half inch of
    snow, it is snowing to the west. If it is snowing to the west, there's a cold front
    coming. If there's a cold front coming, Jack will put his car in the garage this
    evening. So, Jack will put his car in the garage this evening. (Inspired by James
    McMurtry's 'Rachel's Song' from "Where'd You Hide The Body")
                                                                                  Ex—180

(6) (Consider the underlined sentences only. You will need to insert missing premises. Note
    also that the words "and then" are not being used here as a conjunction.) "Once in a
    while maybe you will feel the urge / !To break international copyright law / !By
    downloading MP3s from file-sharing sites / !Like Morpheus or Grokster or Limewire
    or KaZaA / !But deep in your heart you know the guilt would drive you mad! / And
    the shame would leave a permanent scar! / 'Cause you start out stealing songs and
    then you're robbing liquor stores! / And sellin' crack and runnin' over school kids
    with your car!! / So don't download this song! / The record store's where you belong!/
    Go and buy the CD like you know that you should / !Oh, don't download this song."
    ("Weird Al" Jankovic, 'Don't Download This Song' from "Straight Outta Lynnwood")
                                                                                Ex—181

An Introduction To Reasoning
Exercise Set (1) on the Method of Derivation (9 Rules) (12.5)

Part 1. For each set of propositions, fill in the missing information as needed. In every
case, one or more of the conclusion, the rule and the lines used will be supplied and you
must complete the derivation.

(1)
          (1) a ∨ b               Premise
          (2) c & d               Premise
          (3) e ⊃ f               Premise
          (4) _____               ___ Simp.

(2)
          (1) ~a                  Premise
          (2) b ∨ c               Premise
          (3) ______              1, 2 Conj.

(3)
          (1) a ⊃ b               Premise
          (2) c & d               Premise
          (3) f                   Premise
          (4) (c & d) ∨ e         ___ _____


(4)
          (1) g ⊃ n               Premise
          (2) g & k               Premise
          (3) ______              ___ ____
          (4) g ∨ t               ___ ____

(5)
          (1) ~b & a              Premise
          (2) b ∨ (d & c)         Premise
          (3) ~b                  ___ ______
          (4) _______             ___ ______
          (5) d                   ___ ______
                                                                                 Ex—182

Part 2. Use the 9 rules to derive the conclusion indicated from the premises supplied.
(6)
          (1) a ⊃ b                Premise
          (2) a & c                Premise             Concl: a & b




(7)
          (1) (~a ∨ b) ⊃ (c ∨ d)   Premise
          (2) a ⊃ c                Premise
          (3) ~c                   Premise             Concl: d
                                                                                     Ex—183

Part 3. Make a translation key and, writing the propositions in symbolic and using the
following symbols ~ ∨ & ⊃, use the basic six rules plus simplification, conjunction and
addition, to show that the following arguments are valid by the method of derivation.

(8)   If the banana crop is good this season, prices will fall. If the price falls, or oranges
      become more expensive, then banana growers will prosper. Indeed, the crop will
      be good this year, so growers will prosper.




(9)   If Jim is a dog, then Jim is a canine and a mammal. If Jim is either a canine or a
      mammal, he is a vertebrate. Jim is a dog, so, he's a vertebrate.
                                                                                Ex—184

An Introduction To Reasoning
Exercise Set (2) on the Method of Derivation (9 Rules) (12.5)

Part 1. For each set of propositions, fill in the missing information as needed. In every
case, one or more of the conclusion, the rule and the lines used will be supplied and you
must complete the derivation.

(1)
          (1) a ⊃ c               Premise
          (2) c & b               Premise
          (3) c ⊃ a               Premise
          (4) c                   ___ _____

(2)
          (1) d                   Premise
          (2) a ∨ c               Premise
          (3) d & (a ∨ c)         ___ ______


(3)
          (1) e & g               Premise
          (2) _______             1, Add

(4)
          (1) a                   Premise
          (2) ~b                  Premise
          (3) c ⊃ b               Premise
          (4) ______              ___ ______
          (5) ~c & a              ___ ______


(5)
          (1) a ⊃ b               Premise
          (2) s ⊃ g               Premise
          (3) a                   Premise
          (4) ________            ___ ______
          (5) b ∨ g               ___ ______
                                                                                 Ex—185

Part 2. Use the 9 rules to derive the conclusion indicated from the premises supplied.
(6)
          (1) a ⊃ d               Premise.
          (2) b ∨ a               Premise.
          (3) ~b                  Premise.
          (4) g                   Premise.             Concl: d & g




(7)
          (1) (a & b) ⊃ (c ∨ d)   Premise
          (2) (~c ∨ d) ⊃ a        Premise
          (3) (~c ∨ e) ⊃ b        Premise
          (4) ~c & f              Premise              Concl: d




Part 3. Make a translation key and, writing the propositions in symbolic and using the
following symbols ~ ∨ & ⊃, use the basic six rules plus simplification, conjunction and
addition, to show that the following arguments are valid by the method of derivation.
                                                                                      Ex—186



(8)   If gasoline prices rise any further, then people will cut back on their driving and
      alternative sources will be considered, too. If people cut back on their driving, then
      profits at gas stations will fall. Gas prices will rise further. So, not only will prices
      rise, but profits at gas stations will fall.




(9)   If the US Government turns control of some of its ports over to Saudi Arabian
      companies, national security will be compromised. However, National security
      will not be comprised, even though operating costs will be higher. What's more,
      the attitude of the Saudis to the US is often unfriendly and the Saudis are still
      under a Human Rights watch. If the US doesn't turn over control of some of its
      ports to Saudi companies and the Saudi's attitude towards the US is often
      unfriendly, then international tensions will rise. So, either international tensions
      will rise, or the price of oil will increase.
                                                                                Ex—187

An Introduction To Reasoning
Exercise Set (1) on the 9 Rules + DN, Comm., Ass. and DM (12.6)

Part 1. For each set of propositions, complete the derivation as required. In every case,
one or more of the conclusion, the rule and the lines used will be supplied.

(1)
          (1) ~a                  Premise
          (2) (a ∨ c) ∨ d         Premise
          (3) a ∨ (c ∨ d)         ___ ______
          (4) (c ∨ d)             ___ ______

(2)
          (1) a ⊃ c               Premise
          (2) b & c               Premise
          (3) c & b               ___ _____
          (4) c                   ___ _____

(3)
          (1) a                   Premise
          (2) (a ∨ c) ⊃ b         Premise
          (3) a ∨ c               ___ ______
          (4) b                   ___ ______


(4)
          (1) ~(a & ~b)           Premise
          (2) ~d & ~c             Premise
          (3) _________           ___ Comm.

(5)
          (1) a                   Premise
          (2) ~b                  Premise
          (3) c ⊃ b               Premise
          (4) a & ~b              ___ ______
          (5) ~~a & ~b            ___ ______
          (6) ~(~a ∨ b)           ___ ______
                                                                              Ex—188



Part 2. Use the 9 rules + DN, Comm., Ass. and DM to derive the conclusion indicated
from the premises supplied.

(6)
         (1) a ⊃ ~b                    Premise
         (2) b                         Premise             Concl: ~a




(7)
         (1) ~a ⊃ d                    Premise
         (2) ~(a ∨ b)                  Premise             Concl: d & ~b




(8)
         (1) ~a & (b & d)              Premise
         (2) b ⊃ c                     Premise
         (3) ~c                        Premise             Concl: d & b
                                                                                      Ex—189

(9)
       (1) a & d                            Premise
       (2) a ⊃ c                            Premise
       (3) ~b ∨ ~c                          Premise               Concl: ~b




Part 3. Make a translation key and, writing the propositions in symbolic using the
following symbols ~ ∨ & ⊃, use the 9 rules + DN, Comm., Ass. and DM to show that
the following arguments are valid by the method of derivation.

(10) Jack is either a bachelor or is dating Gill. He's not dating Gill. So, he is a bachelor.




(11) If either Jack or Gill or Henry have passed their Board exams, all the hard work
     was worth it. Jack has indeed passed. So, the all the hard work was worth it.
                                                                                   Ex—190

(12) It's not the case that both Bob and Sue will come camping. Sue will come camping,
     so Bob won't.




(13) If the vapor from the solution is not oxygen, the lit splint will not burn when
     inserted into the test tube. The lit splint does burn when inserted into the test tube.
     So, the vapor from the solution is oxygen.
                                                                                Ex—191

An Introduction To Reasoning
Exercise Set (2) on the 9 Rules + DN, Comm., Ass. and DM (12.6)

Part 1. For each set of propositions, complete the derivation as required. In every case,
one or more of the conclusion, the rule and the lines used will be supplied.

(1)
          (1) a                   Premise
          (2) (a ∨ c) ⊃ b         Premise
          (3) a ∨ c               ___ ______
          (4) b                   ___ ______


(2)
          (1) ~(a & ~b)           Premise
          (2) ~d & ~c             Premise
          (3) ~~e                 Premise
          (4) _________           ___ Comm.

(3)
          (1) c ∨ (a ∨ b)         Premise
          (2) (c ∨ a) ∨ b         1 ______
          (3) (a ∨ c) ∨ b         2 ______
          (4) a ∨ (c ∨ b)         3 ______
          (5) a ∨ (b ∨ c)         4 ______

(4)
          (1) ~(c ∨ (f & b))      Premise
          (2) (~c ∨ d) ⊃ ~a       Premise
          (3) ___________         ___ DM
          (4) ___________         ___ ______
          (5) ___________         ___ ______
          (6) ~a                  ___ AA
                                                                           Ex—192

Part 2. Use the 9 rules + DN, Comm., Ass. and DM to derive the conclusion indicated
from the premises supplied.

(5)
         (1) a                        Premise            Concl: b ∨ a




(6)
         (1) ~a                       Premise            Concl: ~(a & b)




(7)
         (1) a ⊃ b                    Premise
         (2) ~(a ∨ b)                 Premise
         (3) g                        Premise            Concl: ~a & g
                                                                          Ex—193

(8)
         (1) (b & d) ⊃ f             Premise
         (2) f ⊃ a                   Premise
         (3) d & ~c                  Premise
         (4) b ∨ c                   Premise            Concl: a




(9)
      (1) (g ∨ w) ⊃ (t & p)          Premise
      (2) ~p                         Premise            Conclusion: ~g




Part 3. Make a translation key and, writing the propositions in symbolic using the
following symbols ~ ∨ & ⊃, use the 9 rules + DN, Comm., Ass. and DM to show that
the following arguments are valid by the method of derivation.
                                                                                     Ex—194



(10) If the Marlins or the Saints won then the Royals will not qualify. The Marlins and
     Bears won, and so did the Raiders. So, the Royals will not qualify.




(11) Either Jack or Gill will fetch the water, or we'll all die of thirst. Jack will not fetch
     the water. So, either Gill will fetch it or we'll all die of thirst.
                                                                              Ex—195

(12) City and Villa are both going on to the next round. If City goes on to the next
     round, Forest will be disappointed. But since either United is not going on to the
     next round or Forest will not be disappointed, United is not going on.
                                                                        Ex—196

An Introduction To Reasoning
Exercise Set (1) on Derivation (9 Rules plus all equivalences) (12.6)

Part 1. Complete the derivation using the hints provided.

(1)
          (1) ~(a & ~b)            Premise
          (2) ~d ⊃ ~c              Premise
          (3) ~~e                  Premise
          (4) _________            ___ DM


(2)
          (1) ~(g & ~d)            Premise
          (2) ~d ⊃ ~c              Premise
          (3) ~~e                  Premise
          (4) _________            ___ Exp.

(3)
          (1) (a & ~f) ⊃ b         Premise
          (2) ~d ⊃ ~c              Premise
          (3) ~~e                  Premise
          (4) _________            ___ Trans.

(4)
          (1) d                    Premise
          (2) a ∨ c                Premise
          (3) ___________          ___ DN
          (4) ___________          ___ DN
          (5) ~(~a & ~c)           ___ ______

(5)
          (1) c                    Premise
          (2) a ∨ ~c               Premise
          (3) ___________          ___ Ass.
          (4) ___________          ___ _____
          (5) a                    ___ _____
                                                                          Ex—197

(6)
          (1) ~(a & ~b)           Premise
          (2) b ∨ ~c              Premise
          (3) a                   Premise
          (4) _________           ___ MI
          (5) ~b                  ___ _____
          (6) _________           ___ DS

(7)
          (1) ~(d & g) ⊃ e        Premise
          (2) d                   Premise
          (3) ~e                  Premise
          (4) ___________         ___ _____
          (5) ___________         ___ _____
          (6) ___________         ___ _____
          (7) g                   ___ _____


Part 2. Derive the conclusion on the right from the premises given:

(8)
      (1) f                       Premise             Conclusion: c ⊃ f




(9)
      (1) ~(a & b)                Premise
      (2) b                       Premise             Conclusion: ~a
                                                       Ex—198

(10)
       (1) (a ∨ b) ⊃ c   Premise
       (2) ~c            Premise   Conclusion: ~b




(11)
       (1) (c & t) ⊃ g   Premise
       (2) c & ~ g       Premise   Conclusion: ~t




(12)
       (1) ~e ⊃ ~l       Premise
       (2) d ⊃ l         Premise   Conclusion: d ⊃ e
                                                                 Ex—199

(13)
       (1) (s & a) ⊃ c      Premise
       (2) ~c               Premise   Conclusion: ~s v ~a




(14)
       (1) ~(~t & ~s)       Premise   Conclusion: t v s




(15)
       (1) ~f ⊃ (r ⊃ t)     Premise
       (2) ~d ∨ ~p          Premise
       (3) f ∨ ~(~d & ~r)   Premise
       (4) ~f               Premise         Conclusion: ~p v t
                                                                                    Ex—200

(16)
       (1) l ⊃ a                   Premise
       (2) a ⊃ c                   Premise
       (3) ~(c ∨ e)                Premise                      Conclusion: ~l




Part 3. Make a translation key and, writing the propositions in symbolic using the
following symbols ~ ∨ & ⊃, use the 9 rules + 8 equivalences to show that the following
arguments are valid by the method of derivation.

(17) If salt raises the freezing point of water, then it is ionic and has a positive valence.
     But it's not the case that salt is both ionic and has a positive valence. So, it either
     doesn't raise the freezing point of water or it doesn't cauterize wounds.




(18) Either Johnson will be fired and Barnes promoted, or, Jackson will be fired and
     Burns will be promoted. Johnson will not be fired, so it's not the case that either
     Johnson will be fired or Jackson will not be.
                                                                                  Ex—201

(19) If Jim is a dog, then Jim is a canine. It's not the case that both Jim is a canine and
     not a mammal. So if Jim is a dog then he's a mammal.
                                                                        Ex—202

An Introduction To Reasoning
Exercise Set (1) on Derivation (9 Rules plus all equivalences) (12.6)

Part 1. Complete the derivation using the hints provided.

(1)
          (1) ~(a ∨ c) & ~b        Premise
          (2) ~e                   Premise
          (3) c ⊃ a                Premise
          (4) __________           ___ DM

(2)
          (1) ~(a ∨ g)             Premise
          (2) ~e                   Premise
          (3) c ⊃ a                Premise
          (4) __________           ___ MI

(3)
          (1) ~a                   Premise
          (2) c ⊃ a                Premise
          (3) __________           ___ Trans.
          (4) c                    ___ _____

(4)
          (1) c & a                Premise
          (2) c ⊃ (a ⊃ b)          Premise
          (3) __________           ___ Exp.
          (4) b                    ___ _____

(5)
          (1) ~(a & ~b)            Premise
          (2) b ⊃ ~c               Premise
          (3) a                           Premise
          (4) _________            ___ DM
          (5) _________            ___ DN
          (6) _________            ___ DN
          (7) b                    ___ DS
                                                                                 Ex—203

(6)
          (1) b ⊃ (a & c)         Premise
          (2) ~a ∨ ~c             Premise
          (3) ___________         ___ _____
          (4) ___________         ___ _____
          (5) ___________         ___ _____
          (6) b ⊃ g               ___ _____


(7)
          (1) ~a ⊃ ~f             Premise
          (2) (f ⊃ a) ⊃ b         Premise
          (3) c ⊃ ~b              Premise
          (4) __________          ___ _____
          (5) __________          ___ _____
          (6) __________          ___ _____
          (7) ~c                  ___ _____

Part 2. Derive the conclusion on the right from the premises given:

(8)
      (1) (a ⊃ b) & (~c ⊃ ~d)            Premise
      (2) a ∨ d                          Premise             Conclusion: b v d




(9)
      (1) ~a                      Premise             Conclusion: a ⊃ b
                                                        Ex—204

(10)
       (1) d ⊃ c          Premise
       (2) ~(c & ~m)      Premise   Conclusion: d ⊃ m




(11)
       (1) o ⊃ (~r ⊃ p)   Premise
       (2) ~(p ∨ r)       Premise   Conclusion: ~o




(12)
       (1) ~l ∨ t         Premise
       (2) t ⊃ r          Premise   Conclusion: l ⊃ r
                                                                Ex—205

(13)
       (1) ~(s & t)            Premise
       (2) t                   Premise   Conclusion: ~s




(14)
       (1) (g ∨ w) ⊃ (t & p)   Premise
       (2) ~p                  Premise   Conclusion: ~g




(15)
       (1) l ⊃ a               Premise
       (2) a ⊃ c               Premise
       (3) ~(c ∨ e)            Premise         Conclusion: ~l
                                                                                        Ex—206

(16)
       (1) (c & t) ⊃ g               Premise
       (2) c & ~ g                   Premise                       Conclusion: ~t




(17)
       (1) ~f ⊃ (r ⊃ t)              Premise
       (2) ~d ∨ ~p                   Premise
       (3) f ∨ ~(~d & ~r)            Premise
       (4) ~f                        Premise                       Conclusion: ~p v t




Part 3. Make a translation key and, writing the propositions in symbolic using the
following symbols ~ ∨ & ⊃, use the 9 rules + 8 equivalences to show that the following
arguments are valid by the method of derivation.

(18) Jack is not here. If Jack isn't here, then Gill is not here and neither is Bob. So, it's not
     the case that Jack or Gill are here.
                                                                                    Ex—207

(19) Both of the following are the case: if Solstice is not on a weekend this year then we
     will have a day off work, and, if New Year's Day is not on a weekend then will we
     will work on New Year's Day. Either Solstice is not on a weekend or New Year's
     Day is not on a weekend. So, either we will we have a day off work, or we will
     work on New Year's Day.




(20) If you accumulate 120 credit hours and have at least a 2.0, you are permitted to
     graduate in May. You have accumulated 120 credit hours but you are not
     permitted to graduate in May. So, you do not have at least a 2.0.




(21) If the price of crude oil rises, then if the government does not have sufficient
     reserves, prices at the pump will rise. It's not the case that either prices at the pump
     will rise or the government has sufficient reserves. So, the price of crude oil will
     not rise.
                                                                                   Ex—208

An Introduction To Reasoning
Exercise Set on Conditional and Indirect Derivation (12.7)

Part 1. Make a translation key and, writing the assertions in symbolic, use a conditional
derivation to show that the following arguments are valid by the method of derivation.

(1)   If it rains, the game is football game will be cancelled. If it rains, the golf outing
      will be cancelled, too. So, if it rains, the game and the outing will be cancelled.




(2)   If standards are lowered and many people apply, then school will be overcrowded.
      If many people apply and school is overcrowded, vandalism on campus will
      increase. So, if standards are lowered and many people apply, vandalism will
      increase.
                                                                                    Ex—209

(3)   If the weather is damp, then if there are slugs, the cabbages will be eaten. If
      temperatures are hot, then if the cabbages are eaten they will shrivel up. If it's true
      that if there are slugs then the cabbage is shriveled up, then, if temperatures are
      hot, frogs will eat any slugs. So, if the weather is damp and temperatures are high,
      birds will eat any slugs.




Part 2. Give a translation key and, writing the propositions in symbolic, use indirect
derivation to show that the following arguments are valid.

(4)   We should not withdraw from Istanistan. Here's why: Imagine we withdraw from
      Istanistan. If we withdraw, the insurgency will become a civil war. If there's a civil
      war, oil prices will go up. But we should not allow oil prices to rise.
                                                                                        Ex—210

(5)   Lying is not morally permissible. Let's assume for a moment that it is permissible
      to lie. If it is permissible to lie, everyone will lie. But if everyone lies then it will be
      impossible to lie. But of course it is possible to lie. So, lying is not morally
      permissible.




(6)   If the President's party controls the House or costs of security at our air- and sea-
      ports increase, then national security has been compromised and public support
      for the President will drop. If support for the President drops or oil prices rise, then
      the President's party will fare poorly on mid-term elections and national security
      has not been compromised. So, the President's party does not control the House.
                                                                                        Ex—211

An Introduction To Reasoning
Exercise Set (1) on Truth Functions (13.2)

For each proposition, underline "T" if it is true and "F" if it is false, when "b" is true, "c" is
false, "d" is true, "e" is false, and "f" is true.

(1)     ~~b




    T     F

(2)     c ⊃ d




    T     F

(3)     (e ∨ ~f) ⊃ d




    T     F

(4)     ~((e & ~f) ⊃ b)




    T     F

(5)     f ⊃ (b ⊃ e)




    T     F
                                           Ex—212

(6)   ~(b ⊃ ~c) & (e ⊃ d)




  T    F

(7)   ~f ∨ (((b ⊃ c) ⊃ (~f & ~e)) ∨ ~~d)




  T    F

(8)   (~b ∨ (b ⊃ c)) ⊃ ((~f & ~e) ∨ ~d)




  T    F
                                                                                        Ex—213

An Introduction To Reasoning
Exercise Set (2) on Truth Functions (13.2)

For each proposition, underline "T" if it is true and "F" if it is false, when "b" is true, "c" is
false, "d" is true, "e" is false, and "f" is true.

(1)     ~b ∨ f




    T     F

(2)     ~b & ~c




    T     F

(3)      (~b ∨ f) & d




    T     F

(4)     c ⊃ (e ⊃ d)




    T     F


(5)     b & (e & c)




    T     F
                                          Ex—214

(6)   ~((b ⊃ ~c) & (e ⊃ d))




  T    F

(7)   (((b ∨ c) ∨ d) ∨ e) & f




  T    F

(8)   (~b ∨ (b ⊃ c)) ⊃ ((~f & ~e) ∨ ~d)




  T    F
                                                                                 Ex—215

An Introduction To Reasoning
Exercise Set (1) on Truth Tables (13.4)

Sample
   Use the truth table method to show that some arbitrary instance of CC is valid.

   (1) a ⊃ b                a      b            a⊃ b          ~b           ~a
   (2) ~b                   T      T             T            F            F
       --------             T      F             F            T            F
   (3) ~a                   F      T             T            F            T
                            F      F             T            T            T

No line has true premises and a false conclusion. So, the argument is valid.


(1) Use the truth table method to show that some arbitrary instance of HS is valid.




(2) Use the truth table method to show that some arbitrary instance of AC is not valid.




(3) Use the truth table method to show that some arbitrary instance of CA is not valid.
                                                                                 Ex—216

(4) Use the truth table method to show that some arbitrary instance of Conj. is valid.




(5) Use the truth table method to show that some arbitrary instance of CD is valid.




(6) Use the truth table method to determine whether the following argument is valid or
    not valid.
       (1) (b ∨ ~c) ⊃ d
       (2) ~c
             ------------------
       (3) d
                                                                              Ex—217

(7) Consider the following argument:

      If national elections deteriorate into television popularity contests, smooth-
      talking morons will get elected. So clearly, smooth-talking morons won't get
      elected if the elections don't deteriorate into television popularity contests.

  (a) Make a translation key for it.




  (b) Relative to the key, translate the argument into symbolic and put it in standard
      form.




  (c) Relative to what you have in standard form, make a truth-table for the argument.




  (d) Relative to your truth-table, is the argument valid or not valid?
                                                                                 Ex—218

An Introduction To Reasoning
Exercise Set (2) on Truth Tables (13.4)

Here are the horseshoe and wedge symbols - copy and paste as needed:
⊃ ∨

(1) Use the truth table method to show that some arbitrary instance of DS is valid.




(2) Use the truth table method to show that some arbitrary instance of CA is not valid.




(3) Use the truth table method to show that some arbitrary instance of Conj. is valid.




(4) Use the truth table method to show that some arbitrary instance of Simp. is valid.
                                                                                Ex—219

(5) Use the truth table method to show that some arbitrary instance of DD is valid.




(6) Use the truth table method to determine whether the following argument is valid or
    not valid.
       (1) ~~b ⊃ (b & ~c)
       (2) b & c
             --------------------
       (3) ~(~~b ⊃ (b & ~c))
                                                                              Ex—220

(7) Consider the following argument:

      If the Yankees win the World Series this year then George will be happy, and
      George will make some trades if he's happy. But George won't be happy
      provided the Yankees don't win it this year. And of course, if George is unhappy,
      he'll make some trades. Thus, George will make some trades.

  (a) Make a translation key for it.




  (b) Relative to the key, translate the argument into symbolic and put it in standard
      form.




  (c) Relative to what you have in standard form, make a truth-table for the argument.




  (d) Relative to your truth-table, is the argument valid or not valid?
                                                                                  Ex—221

An Introduction To Reasoning
Exercise on Logical (In)Equivalence (13.5)

(1) Make a truth table for the propositions "p" and "~~p" and, relative to your truth
    table, determine whether they are logically equivalent or logically inequivalent.




(2) Make a truth table for the propositions "~(b & c)" and "~b ∨ ~c", and, relative to your
    truth table, determine whether they are logically equivalent or logically
    inequivalent.




(3) Make a truth table for the propositions "~(b & c)" and "~b & ~c" and, relative to your
    truth table, determine whether they are logically equivalent or logically
    inequivalent.
                                                                                   Ex—222

(4) Make a truth table for the propositions "b ⊃ c" and "~b ∨ c", and, relative to your
    truth table, determine whether they are logically equivalent or logically
    inequivalent.




(5) Make a truth table for the propositions "p ⊃ (q ⊃ r)" and "(p & q) ⊃ r" and, relative to
    your truth table, determine whether they are logically equivalent or logically
    inequivalent.




(6) Make truth-tables for the sentences "a & (b ∨ c)" and "(a & b) ∨ (a & c)" and, relative
    to your truth-table, determine whether they are logically equivalent or logically
    inequivalent.
                                                                                Ex—223

An Introduction To Reasoning
Exercise (1) on the Targeted Truth Table Method (13.6)

Part 1. For each argument, use a Targeted Truth Table to determine whether it is valid
or invalid.

(1) (1) p ⊃ a
    (2) ~(a ∨ s)
        ----------
    (3) p




(2) (1) t ⊃ s
    (2) s ⊃ b
        -------
    (3) t ⊃ b




Part 2. For each argument, make a translation key, put the argument in standard form
using symbolic and use a Targeted Truth Table to determine whether it is valid or
invalid.

(3) If we paint the plant with soapy water, the aphids will disappear. But it's not the
    case that either the aphids will disappear, or the spider mites. So we will paint the
    plant with soapy water.
                                                                                  Ex—224



(4) If Jack gets more training, he will qualify for the Special Ops unit. If Jack qualifies
    for the Special Ops unit, he will be shipped to Baghdad. So, if Jack gets more
    training, he will be shipped to Baghdad.




(5) If Jack gets more training, he will qualify for the Special Ops unit. If Jack qualifies
    for the Special Ops unit, he will immediately be shipped to Baghdad. So, either Jack
    gets more training or he will not immediately be shipped to Baghdad.
                                                                               Ex—225

An Introduction To Reasoning
Exercise (2) on the Targeted Truth Table Method (13.6)

Part 1. For each argument, use a Targeted Truth Table to determine whether it is valid
or invalid.

(1) (1) t ⊃ s
    (2) s ⊃ b
        -------
    (3) t ∨ ~b




(2)    (1) w
       (2) d ⊃ k
       (3) r ∨ d
           -------
       (4) (w ∨ r) ⊃ d & k




Part 2. For each argument, make a translation key, put the argument in standard form
using symbolic and use a Targeted Truth Table to determine whether it is valid or
invalid.

(3) It's not the case that both soapy water will remove scales and soapy water will kill
    spider mites. So, it's not the case that if soapy water removes scales then soapy
    water kills spider mites.
                                                                                    Ex—226

(4) It can't be that both Tech and State win. But, either one or the other will win. So, it's
    not the case that if Tech wins then State will not.




(5) The gap between rich and poor is widening. If several members of the party defect,
    rich families will be allowed to keep more of their inherited wealth. Either the Estate
    Tax is repealed or several members of the party defect. So, if the gap between rich
    and poor is widening or the Estate Tax is repealed then several members of the
    party defect and rich families will not be allowed to keep more of their inherited
    wealth.
                                                                             Ex—227

An Introduction To Reasoning
Exercise Set (1) on Truth Trees (13.7)

Sample
   Use the truth tree method to show an arbitrary instance of CC is valid.

                                          a⊃b
                                           ~b
                                          ~~a
                                            a
                                   ~a                     b
                                   X                      X

(1) Use the truth tree method to show that AC is invalid.




(2) Use the truth tree method to show that Simp. is valid.




(3) Use the truth tree method to show that DS is valid.
                                                                             Ex—228

(4) Use the truth tree method to show that DD is valid.




(5) Use the truth tree method to determine whether the following argument is valid or
    invalid.
       (1) (b ∨ ~c) ⊃ d
       (2) ~c
             ----------------
       (3) d
                                                                              Ex—229

(6) Consider the following argument:

      If national elections deteriorate into television popularity contests, smooth-
      talking morons will get elected. So clearly, smooth-talking morons won't get
      elected if the elections don't deteriorate into television popularity contests.

  (e) Make a translation key for it.




  (f) Relative to the key, translate the argument into symbolic and put it in standard
      form.




  (g) Relative to what you have in standard form, make a truth tree for the argument.




  (h) Relative to your truth tree, is the argument valid or invalid?
                                                             Ex—230

An Introduction To Reasoning
Exercise Set (2) on Truth Trees (13.7)

(1) Use the truth tree method to show that CA is invalid.




(2) Use the truth tree method to show that Conj. is valid.




(3) Use the truth tree method to show that HS is valid.
                                                                             Ex—231

(4) Use the truth tree method to show that CD is valid.




(5) Use the truth tree method to determine whether the following argument is valid or
    invalid.
       (1) ~~b ⊃ (b & ~c)
       (2) b & c
           ---------------------
       (3) ~(~~b ⊃ (b & ~c))
                                                                              Ex—232

(6) Consider the following argument:

      If the Yankees win the World Series this year then George will be happy, and
      George will make some trades if he's happy. But George won't be happy
      provided the Yankees don't win it this year. And of course, if George is unhappy,
      he'll make some trades. Thus, George will make some trades.

  (e) Make a translation key for it.




  (f) Relative to the key, translate the argument into symbolic and put it in standard
      form.




  (g) Relative to what you have in standard form, make a truth tree for the argument.




  (h) Relative to your truth tree, is the argument valid or invalid?
                                                                                 Ex—233

An Introduction To Reasoning
Exercise Set (1) on Mill's Methods (A7.4-7)

For each passage, make a causation table representing the premises in each argument,
identify a cause or verify the cause suggested by the passage, and name the method the
reasoning is an instance of.

Sample

   Jack's old pair of running shoes, Gill's old pair, and Henry's old pair had different
   designs, were made of different materials, were used on different kinds of terrain,
   and were used in different kinds of weather. The only relevant respect in which they
   agree is being made by Nike. So, the reason why they lasted so long is that they
   were made by Nike.

Cases                     Possible Causes                          Effect
        Design         Terrain   Weather           Nike         Long-Lasting
Jack's     *              *          -                *            *
Gill's     *              -          -                *            *
Henry's    -              *          *                *            *

Cause: Being made by Nike.
      Method: Agreement
      [Note that the premises are vague as to which shoes were of which design and
      were used in which terrain, etc. In such cases, we assign values in the table so
      that the premises are made true (in this case, that they are not all alike with
      respect to each possible cause).]

(1) After a bad streak of fishing trips without success, Jack decided to keep track of his
    routine the next five times he went fishing. On the first, third and fourth trip, he
    brought coffee and sandwiches, while on the others he had coffee along with some
    chips and boiled eggs. The first three times, he fished with worms, while on the last
    two he used lures. The first and last trips were to Antrim Lake, while in between he
    fished the river. Only the second and fourth trip could be called a success.
                                                                                   Ex—234

(2) Three friends, Gill, Jack, and Henry, all recently passed Calc II in their first year of
    college. They went to different high schools; whereas Gill and Jack like math, Henry
    hates it; Henry took the course from professor Reese because he heard he was super-
    clear, and that's where he met Gill and Jack; Gill's GPA is above 3.5, but neither
    Jack's nor Henry's is above 3.0; Gill and Robert are interested in English, while Jack
    is thinking about majoring in anthropology.




(3) All countries in Europe import various raw foods, such as wheat, sugar, soy and
    corn. In the ones that import a lot of sugar the number of cavities per person is high,
    whereas other countries import less sugar and have a lower number of cavities per
    person. No other import shows this same pattern of variation with cavities. So, there
    is some kind of causal connection between sugar-importing and cavities.
                                                                                       Ex—235

(4) Last January, unlike this January, Gill was super positive; this January, unlike last,
    she is paralyzed from the waist down. Hence, since everything else relevant is the
    same, the cause of Gill's negativity this January is her being paralyzed from the
    waist down.




(5) Principles of justified belief must make reference to the processes by which beliefs
    are formed. Here are some types of processes by which people form beliefs: wishful
    thinking, reliance on emotional attachment, mere hunch, hasty generalization,
    perception, remembering, good reasoning, and introspection. Some of these
    processes provide justified beliefs; some do not. The first four processes share the
    feature of unreliability. By contrast, the last four species of belief-forming processes
    are intuitively justification-conferring are reliable (the beliefs they produce are
    generally true). The result, then, is this: The cause of a belief being justified is that it
    was generated by a process which is reliable. (Based on Goldman (1979) p. 9-10)
                                                                                Ex—236

An Introduction To Reasoning
Exercise Set (2) on Mill's Methods (A7.4-7)

For each passage, make a causation table representing the premises in each argument,
identify a cause or verify the cause suggested by the passage, and name the method the
reasoning is an instance of.

(1) Two members of the same family, Bob and Bill, contracted swine flu, but only Bob
    died. Bob is a year older than Bill and they lived in the same town on Long Island.
    They both liked to exercise—Bob played racquetball and Bill played pick-up
    basketball down at the Y. They were about the same weight and ate roughly the
    same diet. Bob was taking medication for a respiratory problem, while Bill had a
    clean bill of health. Both worked full time, Bob in a bank and Bill in an office
    downtown.




(2) Jack, Gill and Henry all failed to turn in their homework for Calc II today. Jack had
    soccer practice after school yesterday, then went home, ate his dinner and watched
    some TV, and then watched the firemen fight the fire that happened down the street.
    Gill went to practice for the school play, then went for fish and chips with some
    friends and then took the bus home. She was so excited about the play she couldn't
    focus on homework and instead spent the evening watching TV. Henry had band
    practice with his rock group. They played one song over and over until they had it
    down. Then he walked home and made rice and dal for dinner. He was thinking
    about washing up, but decided it would be much cooler to make up a song about
    washing up so he spent the evening trying to write some lyrics about dirty dishes.
                                                                                     Ex—237

(3) Last year the grass was super-green, whereas this year it's almost yellow. It didn't
    get any fertilizer last year, and it didn't get any this year, but whereas it got a lot of
    water last year (given all the rain we had), it got almost none this year. Thus,
    probably, the grass's greenness last year was caused by all the water it got.




(4) Twice this past week I [Jack] was late for work. On Monday, my alarm clock had
    wound down over the weekend and I barely got the kids to school on time, never
    mind getting myself to work on time. On Thursday, there was construction on the
    main road going to the school, and I was late getting to work. The other days Gill
    took the kids to school and I went straight to work and was on time. I ran out of gas
    on Wednesday and had to get more, but still made it.
                                                                                 Ex—238

(5) Scientists working at a particle accelerator were puzzled by fluctuations in the
    beams of electrons and positrons that couldn't be explained. It was thought that
    something in the hardware was causing the fluctuations—the power supply, for
    example—but no hardware fault could be found and the power level was the same
    every time an experiment was conducted. Dr. Gerhard Fischer, from the Stanford
    Linear Accelerator Center in California, suggested that the gravitational forces
    exerted by the moon (called lunar effects) might be responsible. A series of four
    experiments in November of 1992 were conducted. The fluctuations in the energies
    of the LEP's particle beams exactly matched fluctuations in the tidal force exerted by
    the moon. Problem solved: the fluctuations in the beams resulted in some way from
    the    fluctuations    in   the    moon's    gravitational    forces.    (Based     on
    http://www.nytimes.com/1992/11/27/us/moon-is-blamed-for-blips-in-a-particle-
    accelerator.html?pagewanted=print)




(6) A big group of my friends and I drove three cars to the concert last night but only I
    got a flat tire. We all took 264W and got off at City Hall Ave, but I took a shortcut
    down Granby St, while they did not (they went on Monticello). That's where I must
    have got the flat.

				
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