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

CATHAL WOODS

2011, 2010

Alike 3.0 License. To view a copy of this license, visit
http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative
Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.
Ex—1

PART 1

DEDUCTIVE REASONING
Ex—2

An Introduction To Reasoning
Exercise Set (1) on Everyday Reasoning (1.1-8) and on Validity & Invalidity (2.1)

1.1-8: For each passage, (i) say whether the conclusion follows from the premises. If not,
explain why not. (ii) Identify the mode of reasoning involved: elimination, chain
argument (with specific propositions), asserting the antecedent (with specific
propositions), Barbara, instantiation, sameness/difference, motion/rest, spatial relation,
temporal relation, symmetricality, transitivity, part-whole, collection, division, other
relation.
2.1: For each inference, say whether it is valid or invalid. Discuss as necessary.

Sample

Politicians get a generous allowance for transportation costs. Enda Kenny is a
politician. So, he gets a generous transportation allowance.

(1.1-8) Follows         Does Not Follow                                 Instantiation
(2.1) Valid             Invalid       If the plural "politicians" is understood to mean "all
politicians" rather than "most", the inference is valid.

(1)      The meeting is at two. The lecture is at three. So, the meeting is first.

Follows           Does Not Follow
Valid             Invalid

(2)      Jack's book is in his room. His room is on the second floor. So, his book is on the
second floor.

Follows           Does Not Follow
Valid             Invalid

(3)      Jack is 5' 7" and Gill is 5' 5". So, Jack is taller than Gill.

Follows           Does Not Follow
Valid             Invalid

(4)      Jack ate the left-over pizza from the fridge. So, the pizza is no longer in the
fridge.

Follows           Does Not Follow
Valid             Invalid
Ex—3
Ex—4

(5)      In a house with a dog. There are feces on the kitchen floor. Only the dog would
poop on the floor. So, the dog pooped.

Follows          Does Not Follow
Valid            Invalid

(6)      Jack is Henry's cousin. Cousins have parents who are either brothers or sisters.
So, their fathers are brothers.

Follows          Does Not Follow
Valid            Invalid

(7)      Glasgow is south of Newcastle, which is south of London. So, London is north of
Glasgow.

Follows          Does Not Follow
Valid            Invalid

(8)      Jack is sitting next to Gill. Gill is wearing a hat. So, Jack is sitting next to someone
in a hat.

Follows          Does Not Follow
Valid            Invalid

(9)      Every time it rains heavily, the back garden floods. It's raining heavily now. So,
the back garden will flood.

Follows          Does Not Follow
Valid            Invalid

(10)     The hall's capacity, for fire safety purposes, is 400 people, but we have admitted
423 people. The hall is dangerously over-full.
Ex—5

Follows   Does Not Follow
Valid     Invalid
Ex—6

(11)   Smith is taller than Jones. Bill is shorter than Smith. So, Jones is taller than Bill.

Follows           Does Not Follow
Valid             Invalid

(12)   Smith is Jones' boss. And Henry is Smith's boss. So, Henry is Jones' boss.

Follows           Does Not Follow
Valid             Invalid

(13)   Henry is worse than Bill at basketball, but Henry is better than Smith. So, Bill is
better than Smith.

Follows           Does Not Follow
Valid             Invalid

(14)   I was talking about John with the glasses, but Jack was talking about John with
the long hair and no glasses. So, we were talking about two different Johns.

Follows           Does Not Follow
Valid             Invalid

(15)   Extra strength Tanqueray (gin) has more alcohol than what I usually drink.
Alcohol causes intoxication. I don't want to get any more intoxicated than usual.
So, I should drink less than normal.

Follows           Does Not Follow
Valid             Invalid
Ex—7

An Introduction To Reasoning
Exercise Set (2) on Everyday Reasoning (1.1-8)

1.1-8: For each passage, (i) say whether the conclusion follows from the premises. If not,
explain why not. (ii) Identify the mode of reasoning involved: elimination, chain
argument (with specific propositions), asserting the antecedent (with specific
propositions), Barbara, instantiation, sameness/difference, motion/rest, spatial relation,
temporal relation, symmetricality, transitivity, part-whole, collection, division, other
relation.
2.1: For each inference, say whether it is valid or invalid. Discuss as necessary.

(1)    Dark clouds are gathering. Dark clouds usually bring rain. So, it will rain soon.

Follows           Does Not Follow
Valid             Invalid

(2)    Jack is next to Gill. So, Gill is next to Jack.

Follows           Does Not Follow
Valid             Invalid

(3)    Gill likes Jack. Jack likes Rocky Road ice-cream. So, Gill likes Rocky Road ice-
cream.

Follows           Does Not Follow
Valid             Invalid

(4)    The Virginia Symphony is not a great orchestra. So, none of its players are great.

Follows           Does Not Follow
Valid             Invalid

(5)    The fire bell is ringing. The fire alarm rings when someone breaks an alarm. So,
someone broke an alarm.
Ex—8

Follows   Does Not Follow
Valid     Invalid
Ex—9

(6)    Jim (the dog) went outside, through the back door. I've been watching the door
and he hasn't come back through it. So, he is still outside.

Follows          Does Not Follow
Valid            Invalid

(7)    There are bear tracks in the mud by the river. Bear tracks are made by bears in
almost every case. So, bears have been by the river.

Follows          Does Not Follow
Valid            Invalid

(8)    Almost every person owns a mobile phone. So, Jack, who is a person, owns a
mobile phone.

Follows          Does Not Follow
Valid            Invalid

(9)    I just passed the final exam. And, if I pass the final exam, I will pass the course. So,
I will pass the course.

Follows          Does Not Follow
Valid            Invalid

(10) I'll sign up for either a pottery course or a painting course. (Later:) The pottery
course is full. So, I guess I'll take the painting course.

Follows          Does Not Follow
Valid            Invalid

(11) Jack is close to the pond. The pond is close to the playground. So, Jack is close to
the playground.

Follows          Does Not Follow
Ex—10

Valid   Invalid
Ex—11

(12) Cherry blossom tress only bloom in the spring. The cherry blossom trees are
blossoming. So, it is spring.

Follows           Does Not Follow
Valid             Invalid

(13) At a square, four person, table, Jack is sitting across from Gill and Henry is on his
right. Gill is on Bill's left. So, the order of people is Henry, Bill, Gill, Jack.

Follows           Does Not Follow
Valid             Invalid

(14) Smoking pot causes me to be really groggy the next day. I don't want to be groggy
tomorrow. So, I won't smoke up this evening.

Follows           Does Not Follow
Valid             Invalid

(15) I'm going to be groggy tomorrow. I'm smoking pot and smoking pot causes me to
be really groggy the next day.

Follows           Does Not Follow
Valid             Invalid

(16) There's always a good deal of truth to a cliché. The saying "One man's meat is
another man's poison" is a cliché. So, there's a good deal of truth to the saying "One
man's meat is another man's poison".

Follows           Does Not Follow
Valid             Invalid
Ex—12

An Introduction To Reasoning
Exercise Set (1) on Logically Structured English (2.2-4)

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

b:   Jack is a bachelor.
g:   Gill will go out with Jack.
h:   Jack has a good sense of humor.
l:   Jack likes the outdoors.
m:   Jack is married.
s:   Jack says that he is a bachelor.
t:   Jack is tall.

(1) Either Jack is a bachelor or he is married.

(2) Jack does not like the outdoors.

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

(4) Jack is not married, and Gill will go out with Jack.
Ex—13

(5) If Jack is unmarried, then Gill will go out with him.
Ex—14

(6) Although Jack isn't married, Gill will not go out with him.

(7) Jack is not both tall and likes the outdoors.

(8) It's not the case that Jack either likes the outdoors or has a good sense of humor.

(9) If Jack is tall or likes the outdoors, then, if he is a bachelor, then Gill will go out with
him.

(10) Either Jack is married and Gill won't go out with him, or he is bachelor and she will.
Ex—15

An Introduction To Reasoning
Exercise Set (2) on Logically Structured English (2.2-4)

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

b:   Jack is a bachelor.
g:   Gill will go out with Jack.
h:   Jack has a good sense of humor.
l:   Jack likes the outdoors.
m:   Jack is married.
s:   Jack says that he is a bachelor.
t:   Jack is tall.

(1) Jack is tall.

(2) Jack is a tall bachelor.

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

(4) Jack neither is a bachelor nor says he's a bachelor.
Ex—16

(5) If he's a bachelor, Jack is unmarried.

(6) If Jack likes the outdoors and says he's a bachelor, then Gill will go out with him.

(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.

(9) Jack is tall and has a good sense of humor and likes the outdoors.

(10)   Jack is either tall or has a good sense of humor, but not both.
Ex—17

An Introduction To Reasoning
Exercise (1) on Logically Structured English (2.2-5)

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.
g:   Gill will go out with Jack.
h:   Jack has a good sense of humor.
l:   Jack likes the outdoors.
m:   Jack is married.
s:   Jack says that he is a bachelor.
t:   Jack is tall.

(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.
Ex—18

(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—19

(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.

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

(9) If Jack is tall, likes the outdoors and has a good sense of humor, Gill will go out with
him.

(10) If Jack has any of the three qualities—tall, likes the outdoors, has a good sense of
humor—then Gill will go out with him.
Ex—20

An Introduction To Reasoning
Exercise (2) on Logically Structured English (2.2-5)

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.
g:   Gill will go out with Jack.
h:   Jack has a good sense of humor.
l:   Jack likes the outdoors.
m:   Jack is married.
s:   Jack says that he is a bachelor.
t:   Jack is tall.

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

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

(3) Jack's being tall, together with his liking the outdoors, is sufficient for Gill's going
out with him.

(4) Gill will go out with Jack if and only if he's a tall bachelor.
Ex—21

(5) Provided that Jack says he's a bachelor, Gill will go out with him.
Ex—22

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

(7) Only if Jack is a bachelor and either likes the outdoors or is tall will Gill go out with
him.

(8) If Jack has any two of the three qualities—tall, likes the outdoors, has a good sense
of humor—then Gill will go out with him.
Ex—23

An Introduction To Reasoning
Exercise Set (1) on 4 of the Big 8 (3.3-7)

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 inference is 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.
Ex—24

AA   AC   CC   CA   Valid   Not valid
Ex—25

(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.
Ex—26

AA   AC   CC   CA   Valid   Not valid
Ex—27

An Introduction To Reasoning
Exercise Set (2) on 4 of the Big 8 (3.3-7)

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 inference is 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 comes.
However, it's not the case that either Smith or Jones can 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—28

(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.
Ex—29

AA   AC   CC   CA   Valid   Not valid
Ex—30

An Introduction To Reasoning
Exercise Set (1) on the Big 8 (3.3-10)

For each passage (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 inference is an instance of AA, AC, CC, CA, Chain,
Elim., 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     Chain Elim. 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     Chain Elim. CD      DD            Valid Not valid
Ex—31

(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     Chain Elim. 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     Chain Elim. 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.
Ex—32

AA AC        CC     CA     Chain Elim. CD        DD            Valid Not valid
(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     Chain Elim. CD        DD            Valid Not valid
Ex—33

An Introduction To Reasoning
Exercise Set (2) on the Big 8 (3.3-10)

For each passage (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 inference is an instance of AA, AC, CC, CA, Chain,
Elim., 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     Chain Elim. 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     Chain Elim. CD       DD            Valid Not valid
Ex—34

(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     Chain Elim. 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     Chain Elim. 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.
Ex—35

AA   AC   CC   CA   Chain Elim. CD   DD   Valid Not valid
Ex—36

An Introduction To Reasoning
Exercise Set (1) on Logically Structured Symbolic Propositions (4.2)

Part 1
For each proposition, underline "Yes" if it is well-formed and "No" if it is not well-
formed. If you underline "No", explain the problem.

(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—37

(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 passage, make a translation key and translate the propositions 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 come camping.
Ex—38

(12)   If either Bob or Alice come camping, Xena will come camping too.
Ex—39

An Introduction To Reasoning
Exercise Set (2) on Logically Structured Symbolic Propositions (4.2)

Part 1
For each proposition, underline "Yes" if it is well-formed and "No" if it is not well-
formed. If you underline "No", explain the problem.

(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.
Ex—40

(6) Either Jack is married or he's not, and either Gill will go out with him or she won't.
Ex—41

(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 proposition, 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—42

(12) Being the all-time goal-scorer is sufficient for being admitted to the football hall
of fame.
Ex—43

An Introduction To Reasoning
Exercise Set (1) on the Method of Derivation (6 Rules) (4.3)

For each passage, give a translation key and show that the inference is 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—44

(3)   If this creature has eight legs, it is not an ant. It has eight legs. So, it is not an ant.

(4)   Jack is either drunk or extremely tired. He isn't drunk. So, he is extremely tired.

(5)   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. She'll either stay in tonight
or not. So, she'll either get up tomorrow morning at six or not get up until nine.

(6)   Jack has a Raiders hat and a Raiders foam finger. If Jack has a Raiders hat and a
Raiders foam finger, he is a Raiders fan. If Jack is a Raiders fan, he won't get along
with Gill, who is a 49ers fan. So, Jack won't get along with Gill, who is a 49ers fan.
Ex—45
Ex—46

An Introduction To Reasoning
Exercise Set (2) on the Method of Derivation (6 Rules) (3.3)

For each passage, give a translation key and show that the inference is 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 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.

(3) If too many people withdraw from the market, confidence will plummet. If
confidence plummets, investment will dry up. So, if too many people withdraw
from the market, investment will dry up.
Ex—47
Ex—48

(4) Jack and Jim are at the park. If they are at the park, they can pick up some milk on
the way home. So, they can pick up some milk on the way home.

(5) Unless Jack is willing to drive us, we can’t go to the movies. Jack is not willing to
drive us. So, we can't go to the movies. If we can't go to the movies, we will go the
ikebana session. So, we will go to the ikebana session.

(6) Jack is fishing or doing logic on his porch. He is not doing logic on his porch. So, he
is fishing. If Jack is fishing, he left Jim will Gill. So, Jack left Jim with Gill.
Ex—49
Ex—50

An Introduction To Reasoning
Exercise Set (1) on Passages Without Interim Conclusions (6 Rules) (4.4)

For each passage, give a translation key and show that the conclusion can be reached
validly 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 can easily clean up his mess. Only if we have a
pooper-scooper can we easily clean up his miss. But we don't have a pooper-
scooper. So, no park for Jim.

g = Jim can go to the park.
e = We can easily clean up Jim's mess.
p = We have a pooper-scooper.

(1) g  e            Premise
(2) e  p            Premise
(3) ~p               Premise                                   Conclusion: ~g
(4) g  p            1, 2 Chain
(3) ~g               4, 3 CC

(1) If Jack is a bachelor, then, if he has a good sense of humor, Gill will go out with him.
He is a bachelor. He has a good sense of humor. So, Gill will go out with him.

(2) Either the Chargers or the Daredevils will win this weekend. If either team wins, the
Super Kings will not make it to the playoffs. And if the Super Kings don't make it,
no team from south India will be in the playoffs. So, no team from south India will
be in the playoffs.
Ex—51

(3) 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")

(4) If this solution can neutralize bases, it can be used to remove cuticles. But this
solution cannot remove cuticles. So, it cannot neutralize bases. 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.
Ex—52

An Introduction To Reasoning
Exercise Set (2) on Passages Without Interim Conclusions (6 Rules) (4.4)

For each passage, give a translation key and show that the conclusion can be reached
validly by the method of derivation (writing the propositions in symbolic), using only
the basic six rules.

(1) 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. And there are indeed
holes. So, there are no trails of slime.

(2) Provided that McIlroy taps in that excellent second shot to the fifteenth for birdie, he
will move four shots clear of the field. At four shots clear, it will be very difficult for
anyone to catch him at this late stage. A moment later: There it is—an easy birdie for
McIlroy. So, it will be very difficult for anyone to catch him at this late stage.

(3) If you start out downloading songs, then you'll be robbing liquor stores. And  if you
rob liquor stores, next thing you know you'll be sellin' crack.   You definitely won't
be selling crack. So, you won't download this song . (Based on "Weird Al" Jankovic,
'Don't Download This Song' from "Straight Outta Lynnwood")
Ex—53
Ex—54

(4) Jack's drinking a fifth of vodka is sufficient for getting him drunk. He isn't drunk.
There is an empty fifth of vodka and an empty bottle of wine on the table. Jack must
be drinking the wine.

(5) 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.

(6) Smith is out of money unless he got a job recently. He's spending money on drinks
for his friends at the St. James Tavern. And so, he must have gotten a job recently.
Ex—55
Ex—56

An Introduction To Reasoning
Exercise Set (1) on the Method of Derivation (9 Rules) (4.3-5)

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
Ex—57

(3) ~b        ___ ______
(4) _______   ___ ______
(5) d         ___ ______
Ex—58

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

(7)
(1) (~a  b)  (c  d)   Premise
(2) a  c                Premise
(3) ~c                   Premise             Conclusion: d
Ex—59

Part 3. For each argument, 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 inference is 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—60

An Introduction To Reasoning
Exercise Set (2) on the Method of Derivation (9 Rules) (4.3-5)

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
Ex—61

(4) ________   ___ ______
(5) b  g      ___ ______
Ex—62

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.             Conclusion: d & g

(7)
(1) (a & b)  (c  d)   Premise
(2) (~c  d)  a        Premise
(3) (~c  e)  b        Premise
(4) ~c & f              Premise              Conclusion: d
Ex—63

Part 3. For each argument, 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 conclusion follows validly by
the method of derivation.
Ex—64

(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—65

An Introduction To Reasoning
Exercise Set (1) on the Method of Derivation (9 + 4 Rules) (4.3-4.6.6)

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
Ex—66

(3) c  b               Premise
(4) a & ~b              ___ ______
(5) ~~a & ~b            ___ ______
(6) ~(~a  b)           ___ ______
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             Conclusion: ~a

(7)
(1) ~a  d                    Premise
(2) ~(a  b)                  Premise             Conclusion: d & ~b

(8)
(1) ~a & (b & d)              Premise
Ex—67

(2) b  c   Premise
(3) ~c      Premise   Conclusion: d & b
Ex—68

(9)
(1) a & d                            Premise
(2) a  c                            Premise
(3) ~b  ~c                          Premise               Conclusion: ~b

Part 3. For each argument, 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 conclusion follows validly 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—69

(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—70

An Introduction To Reasoning
Exercise Set (2) on the Method of Derivation (9 + 4 Rules) (4.3-4.6.6)

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—71

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

(5)
(1) a                        Premise            Conclusion: b  a

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

(7)
(1) a  b                    Premise
(2) ~(a  b)                 Premise
(3) g                        Premise            Conclusion: ~a & g
Ex—72

(8)
(1) (b & d)  f      Premise
(2) f  a            Premise
(3) d & ~c           Premise
(4) b  c            Premise   Conclusion: a

(9)
(1) (g  w)  (t & p)   Premise
(2) ~p                  Premise   Conclusion: ~g
Ex—73

Part 3. For each argument, 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 inference is valid by the method of derivation.
Ex—74

(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—75

(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.

(13) If Jack has a good sense of humor or is interesting to talk to, Gill will go out with
him. He doesn't have a good sense of humor. He is not interesting to talk to. So,
Gill won't go out with him
Ex—76

An Introduction To Reasoning
Exercise Set (1) on the Method of Derivation (9 + 7 Rules) (4.3-4.6.7)

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) _________            ___ Trans.

(3)
(1) (a & ~f)  b         Premise
(2) d  (~c & b)         Premise
(3) (~e & f) & g         Premise
(4) _________            ___ Exp.

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

(5)
(1) c                    Premise
(2) a  ~c               Premise
Ex—77

(3) ___________   ___ Comm.
(4) ___________   ___ _____
(5) a             ___ _____
Ex—78

(6)
(1) ~(a & ~~b)          Premise
(2) b  ~c              Premise
(3) a                   Premise
(4) _________           ___ MI
(5) ~b                  ___ _____
(6) _________           ___ Elim.

(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—79

(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—80

(13)
(1) (s & a)  c      Premise
(2) ~c               Premise   Conclusion: ~s  ~a

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

(15)
(1) ~f  (r  t)     Premise
(2) ~d  ~p          Premise
(3) f  ~(~d & ~r)   Premise
(4) ~f               Premise         Conclusion: ~p  t
Ex—81

(16)
(1) l  a                   Premise
(2) a  c                   Premise
(3) ~(c  e)                Premise                      Conclusion: ~l

Part 3. For each argument, make a translation key and, writing the propositions in
symbolic using the following symbols ~  & , use the 9 rules of inference + 7 rules of
equivalence to show that the inference is 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—82

(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—83

An Introduction To Reasoning
Exercise Set (2) on the Method of Derivation (9 + 7 Rules) (4.3-4.6.7)

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
Ex—84

(6) _________   ___ DN
(7) b           ___ Elim.
Ex—85

(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—86

(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—87

(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—88

(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  t

Part 3. For each argument, make a translation key and, writing the propositions in
symbolic using the following symbols ~  & , use the 9 rules of inference + 7 rules of
equivalence to show that the inference is 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—89

(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—90

An Introduction To Reasoning
Exercise Set on Conditional and Indirect Derivation (4.7)

Part 1. For each argument, make a translation key and, writing the assertions in
symbolic, use a conditional derivation to show that the inference is 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—91

(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. For each argument, give a translation key and, writing the propositions in
symbolic, use indirect derivation to show that the inference is 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—92

(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—93

An Introduction To Reasoning
Exercise Set (1) on Truth Functions (5.2)

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—94

(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—95

An Introduction To Reasoning
Exercise Set (2) on Truth Functions (5.2)

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—96

(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—97

An Introduction To Reasoning
Exercise Set (1) on Truth Tables (5.3-4)

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 inference is valid.

(1) Use the truth table method to show that some arbitrary instance of Chain 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—98

(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 inference is valid or
not valid.
(1) (b  ~c)  d
(2) ~c
------------------
(3) d
Ex—99

(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.
Ex—100

(d) Relative to your truth-table, is the inference valid or not valid?
Ex—101

An Introduction To Reasoning
Exercise Set (2) on Truth Tables (5.3-4)

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 Elim. 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—102

(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 inference is valid or
not valid.
(1) ~~b  (b & ~c)
(2) b & c
--------------------
(3) ~(~~b  (b & ~c))
Ex—103

(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.
Ex—104

(d) Relative to your truth-table, is the inference valid or not valid?
Ex—105

An Introduction To Reasoning
Exercise Set on Logical (In)Equivalence (5.5)

(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—106

(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—107

An Introduction To Reasoning
Exercise (1) on the Targeted Truth Table Method (5.6)

Part 1. For each argument, use a Targeted Truth Table to determine whether the
inference 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 the inference 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—108

(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—109

An Introduction To Reasoning
Exercise (2) on the Targeted Truth Table Method (5.6)

Part 1. For each argument, use a Targeted Truth Table to determine whether the
inference 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 the inference 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—110

(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—111

An Introduction To Reasoning
Exercise Set (1) on Truth Trees (5.7)

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 an arbitrary instance of AC is invalid.

(2) Use the truth tree method to show that an arbitrary instance of Simp. is valid.

(3) Use the truth tree method to show that an arbitrary instance of Elim. is valid.
Ex—112

(4) Use the truth tree method to show that an arbitrary instance of DD is valid.

(5) Use the truth tree method to determine whether the following inference is valid or
invalid.
(1) (b  ~c)  d
(2) ~c
----------------
(3) d
Ex—113

(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.
Ex—114

(h) Relative to your truth tree, is the inference valid or invalid?
Ex—115

An Introduction To Reasoning
Exercise Set (2) on Truth Trees (5.7)

(1) Use the truth tree method to show that an arbitrary instance of CA is invalid.

(2) Use the truth tree method to show that an arbitrary instance of Conj. is valid.

(3) Use the truth tree method to show that an arbitrary instance of Chain is valid.
Ex—116

(4) Use the truth tree method to show that an arbitrary instance of CD is valid.

(5) Use the truth tree method to determine whether the following inference is valid or
invalid.
(1) ~~b  (b & ~c)
(2) b & c
---------------------
(3) ~(~~b  (b & ~c))
Ex—117

(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.
Ex—118

(h) Relative to your truth tree, is the inference valid or invalid?
Ex—119

An Introduction To Reasoning
Exercise Set (1) on Categorical Logic (6.5)

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—120

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 inference
valid?
Ex—121

(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 inference
valid?
Ex—122

(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 inference
valid?
Ex—123

(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 inference
valid?
Ex—124

(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 inference
valid?
Ex—125

(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 inference
valid?
Ex—126

An Introduction To Reasoning
Exercise Set (2) on Categorical Logic (6.5)

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—127

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 inference
valid?
Ex—128

(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 inference
valid?
Ex—129

(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 inference
valid?
Ex—130

(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 inference
valid?
Ex—131

(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 inference
valid?
Ex—132

(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 inference
valid?
PART 2

REASONING IN THE WILD
Ex—134

An Introduction To Reasoning
Exercise Set (1) on Reasoning, Flag Words (7.1-4)

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".)

134
Ex—135

Arguing   Explaining         Neither

135
Ex—136

(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)

136
Ex—137

Arguing   Explaining         Neither

137
Ex—138

(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

138
Ex—139

An Introduction To Reasoning
Exercise Set (2) on Reasoning, Flag Words (7.1-4)

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.

139
Ex—140

Arguing   Explaining         Neither

140
Ex—141

(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.

141
Ex—142

Arguing   Explaining         Neither

142
Ex—143

(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

143
Ex—144

An Introduction To Reasoning
Exercise Set (1) on Propositions (7.5)

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 premises/explainers 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.

144
Ex—145

Arguing   Explaining

145
Ex—146

(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.

146
Ex—147

Arguing   Explaining

147
Ex—148

(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

148
Ex—149

An Introduction To Reasoning
Exercise Set (2) on Propositions (7.5)

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 premises/explainers 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

149
Ex—150

150
Ex—151

(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

Arguing             Explaining

151
Ex—152

(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

152
Ex—153

An Introduction To Reasoning
Exercise Set (1) on the Two Criteria (8.1)

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 passage, (i) underline the explainee or conclusion, (ii) put any flag
words in (parentheses), (iii) [bracket] the premises/explainers, (iv) make note of any
needed changes or write out the propositions in full, and (v) number the propositions.
(vi) Put the argument or explanation into standard form. Use "J" or "E" to denote an
argument or explanation.
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)

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

153
Ex—154

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.

(6) 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.

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

(8) 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)

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Ex—155

(9) 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.

(10)   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.

155
Ex—156

(11) 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.

(12) 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.

(13) Doing marijuana would be bad. You shouldn't do marijuana. (Based on South
Park 204)

156
Ex—157

(14) 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.

(15) 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.

157
Ex—158

An Introduction To Reasoning
Exercise Set (2) on the Two Criteria (8.1)

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 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) Put the
argument or explanation into standard form. Use "J" or "E" to denote an argument or
explanation.
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.

(6) 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.

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Ex—159

(7) 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.

(8) 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!

159
Ex—160

(9) 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.

(10) 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.

(11) 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.

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Ex—161

(12)   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?

(13) 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.

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Ex—162

(14) 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 )

(15) 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 )

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Ex—163

(16) The consequence of not running good military academies is having a bad
military. Highly armed, under-educated officer corps are a recipe for despotism and
deadly accidents in the field. So, military academies absolutely have to work.
college.html )

163
Ex—164

An Introduction To Reasoning
Exercise Set (1) on Getting Clear on the Meaning (8.2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (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.

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Ex—165

(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

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Ex—166

(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.

166
Ex—167

(9)

(10)

167
Ex—168

An Introduction To Reasoning
Exercise Set (2) on Getting Clear On The Meaning (8.2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (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?

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Ex—169

(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.

169
Ex—170

(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)

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Ex—171

(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!

171
Ex—172

An Introduction To Reasoning
Exercise Set (1) on Sources (8.3)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (iv) make note of any needed
changes or write out the propositions in full, and (v) number the propositions. (vi) Put
the reasoning in standard form. (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

172
Ex—173

metabolism.

173
Ex—174

(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.

174
Ex—175

(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.

175
Ex—176

An Introduction To Reasoning
Exercise Set (2) on Sources (8.3)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (iv) make note of any needed
changes or write out the propositions in full, and (v) number the propositions. (vi) Put
the reasoning in standard form. (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."

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Ex—177

(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.

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Ex—178

(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!

178
Ex—179

An Introduction To Reasoning
Exercise Set (1) on Reason Substitutes (9.1-2)

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!

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Ex—180

(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.

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Ex—181

(8) A comment on an article by Jonah Goldberg against state "health coach" programs: What I
find creepy is that Goldberg has no problem with government sticking its nose in its
citizens' bedrooms or wiretapping its citizens' phone calls, but now suddenly, he has
a problem?
(http://www.philly.com/philly/opinion/20110130_N_J__health_efforts_might_not
_be_so_hot.html )

181
Ex—182

An Introduction to Reasoning
Exercise (2) on Reason Substitutes Really Bad Reasoning (9.1-3)

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 13.1-3. 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!

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Ex—183

(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!

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Ex—184

(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.

184
Ex—185

(10) There is a lot of positive talk concerning parenthood because people tend to
think about the positive effects that have a child brings and they ten to exclude the
numerous negatives that it brings.

(11) 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.

185
Ex—186

An Introduction To Reasoning
Exercise Set (1) on Adding Warrants (To Arguments) (10.2)

For each argument, (i) underline the 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) Put the reasoning in standard
form. Make the reasoning explicit by (vii) adding in writing any warrants, marked with
an asterisk. Add the new premise(s) to your standard form. (viii) Say whether the
reasoning is valid or cogent. (ix) Say whether the premises, including any you added,
are true, as far as you know. Add explanations at any point if necessary.

Sample
(1) What a scumbag! (2) [Thomson deliberately caused the accident] and then (3)
[sued the other driver.]

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

(vii) Valid.
seems good to me (though "scumbag" is a somewhat imprecise term).

(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.

186
Ex—187

187
Ex—188

(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.

188
Ex—189

(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.

189
Ex—190

An Introduction To Reasoning
Exercise Set (2) on Adding Warrants (To Arguments) (10.2)

For each argument, (i) underline the 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) Put the reasoning in standard
form. Make the reasoning explicit by (vii) adding in writing any warrants, marked with
an asterisk. Add the new premise(s) to your standard form. (viii) Say whether the
reasoning is valid or cogent. (ix) 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.

190
Ex—191

(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.

191
Ex—192

(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.

192
Ex—193

An Introduction To Reasoning
Exercise Set (3) on Adding Warrants (10.2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (iv) make note of any needed
changes or write out the propositions in full, and (v) number the propositions. (vi) Put
the reasoning in standard form. Use "J" or "E" to denote an argument or explanation.
Make the reasoning explicit by (vii) adding in writing any warrants, marked with an
asterisk. Add the new premise(s) to your standard form. (viii) If an argument, say
whether the reasoning is valid or cogent; if an explanation, say whether the reasoning is
satisfying. (ix) Say whether the premises, including any you added, are true, as far as
you know. Add explanations at any point if necessary.

(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.

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Ex—194

(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.

194
Ex—195

(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, and it comes from Russia,
which is also where the spent uranium will return, and the process will be watched
closely by the UN's atomic agency. ( http://www.bbc.co.uk/news/world-middle-
east-11046174 )

195
Ex—196

An Introduction To Reasoning
Exercise Set (4) on Adding Warrants (10.2)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (iv) make note of any needed
changes or write out the propositions in full, and (v) number the propositions. (vi) Put
the reasoning in standard form. Use "J" or "E" to denote an argument or explanation.
Make the reasoning explicit by (vii) adding in writing any warrants, marked with an
asterisk. Add the new premise(s) to your standard form. (viii) If an argument, say
whether the reasoning is valid or cogent; if an explanation, say whether the reasoning is
satisfying. (ix) Say whether the premises, 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.

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Ex—197

(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.

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Ex—198

(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/ )

198
Ex—199

An Introduction To Reasoning
Exercise Set (1) on Standard Forms & Diagrams (11.1)

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) give a 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—200

(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—201
Ex—202

(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—203

An Introduction To Reasoning
Exercise Set (2) on Diagrams (11.1)

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) give a 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—204

(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—205
Ex—206

(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—207

An Introduction To Reasoning
Exercise Set (1) on Complex Reasoning (11.2-4)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (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.

1+2
(4) = Potatoes are cheap.
(5) = You should include potatoes in your diet.

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.

(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.
Ex—208
Ex—209

(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.

(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.
Ex—210

(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)

(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.
Ex—211

(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.

(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—212

An Introduction To Reasoning
Exercise Set (2) on Complex Reasoning (11.2-4)

For each passage, (i) underline the explainee or conclusion, (ii) put any flag words in
(parentheses), (iii) [bracket] the premises/explainers, (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—213

(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—214

(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—215

(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—216

An Introduction To Reasoning
Exercise Set (1) on Objections & Rebuttals (11.5-6)

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,
Ex—217

(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—218

(4) Read the article at http://www.bbc.co.uk/news/technology-12817083 about a
possible trademark violation. Present the argument given in the lawsuit from Apple
and (as an objection) the reply by the spokesman for Microsoft.

(5) 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—219

An Introduction To Reasoning
Exercise Set (2) on Objections & Rebuttals (11.5-6)

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
reasons-for-holiday-cheer.html)
Ex—220

(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—221

(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—222

An Introduction To Reasoning
Exercise (1, 2) on Very Long Passages (11.7)

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.
Ex—223

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.
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.

Evaluation
….
PART 3

INDUCTIVE & SCIENTIFIC REASONING
Ex—225

An Introduction To Reasoning
Exercise Set (1) on Valid, Cogent, Incogent (12.1-2)

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 inference is valid, cogent, or incogent and explain your answer.

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 must have a
vitamin K deficiency.

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

(1) 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.

(2) 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.

(3) 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.

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

225
Ex—226

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

(6) 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.

(7) 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.

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

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

226
Ex—227

(10) 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.

(11) 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.

(12) 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.

(13) 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.

227
Ex—228

(14) 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.

(15) 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.

228
Ex—229

An Introduction To Reasoning
Exercise Set (2) on Valid, Cogent, Incogent (12.1-2)

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 inference is valid, cogent, or incogent and explain your answer.

(1) 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.

(2) 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).

(3) 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.

(4) 90% of the marbles in the box are blue. So, about 90% of the 20 I pick at random will
be blue.

229
Ex—230

(5) 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.

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

(7) 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.

(8) 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.

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

230
Ex—231

(10)    (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.

(11) 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.

(12) 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.

(13) 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.

(14) 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.

231
Ex—232

(15) 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.

232
Ex—233

An Introduction To Reasoning
Exercise Set (1) on Inductive Generalization (12.3)

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 inference 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.

233
Ex—234

(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.

234
Ex—235

(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.

235
Ex—236

An Introduction To Reasoning
Exercise Set (2) on Inductive Generalization (12.3)

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 inference 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

(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.

236
Ex—237

(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.

237
Ex—238

(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.

238
Ex—239

(7) Reconstruct and comment on the inference described below in 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).

(8) Reconstruct and comment on the inference described below in a famous poll. What
might have gone wrong?

A Gallup poll predicted that Thomas
Dewey      would win the U.S.
presidential election of 1948, but his
opponent, Harry S. Truman, carried
50% of the vote to Dewey's 45%. The
sample was 3250 American adults,
selected by a "quota" method: the
number of men and women, rural
and urban voters, and voters from
different races, was proportional to
the census of 1940.

(Image: Truman holds a copy of a newspaper, printed
in advance of the results, announcing his defeat!)

239
Ex—240

An Introduction To Reasoning
Exercise Set (1) on Instantiation Syllogism, Induction to a Particular (12.3-5)

For each argument, (i) put the argument in standard form, including the warrants
needed to make the inference 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
inference is incogent, explain why.

Sample

There is only a 10% chance of a frost in Wilmington, North Carolina, on April 1st in
any year. Today is April 1st, so there won't be a frost tonight.

IG       IS      IP

(1) 10% of April 1sts are days with a frost.
(2) Today is an April 1st.
(3) This April 1st is a typical April 1st with respect to frost.*
-------------------------------------------------------------------------
(4) There won't be a frost on this April 1st.

(iii) In this made-up example, we do not know anything about the day in question.

(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

240
Ex—241

(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

241
Ex—242

(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

242
Ex—243

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

IG     IS     IP

243
Ex—244

An Introduction To Reasoning
Exercise Set (2) on Instantiation Syllogism, Induction To A Particular (12.3-5)

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
inference 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

244
Ex—245

(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

IG     IS     IP

245
Ex—246

(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

246
Ex—247

(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

247
Ex—248

An Introduction To Reasoning
Exercise Set (1) on Correlation (13.1)

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.

248
Ex—249

(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.

249
Ex—250

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.

250
Ex—251

An Introduction To Reasoning
Exercise Set (2) on Correlation (13.1)

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.
My printer at home is broken.

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

(3) He is good at basketball.
He is black.

251
Ex—252

(4) The beach is closed to swimmers.
A shark had been sighted earlier in the morning.

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

(6) The power just went out.
A violent storm is raging.

252
Ex—253

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.

253
Ex—254

An Introduction To Reasoning
Exercise Set (1) on Evaluating Explanations (13.2)

For each passage, (i) say whether or not the explainee is not correlated with, correlated
but not explained/caused by, or, both correlated with and explained/caused by, the
explainer. (ii) Explain your answer, perhaps making mention of the strength of the
correlation and the two warrants needed for explanation/causation.

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) 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.

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

254
Ex—255

(3) There is wind because the trees move back and forth.

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

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

255
Ex—256

(6) There are two explanations in the following: 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.

(7) Evaluate each of the two explanations in the following: I was late to class because traffic
was terrible. It was terrible because Main Street was closed for road repairs.

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

256
Ex—257

257
Ex—258

An Introduction To Reasoning
Exercise Set (2) on Evaluating Explanations (13.2)

For each passage, (i) say whether or not the explainee is not correlated with, correlated
but explained/caused by, or, both correlated with and explained/caused by, the
explainer. (ii) Explain your answer; include a discussion of the strength of the
correlation and the two warrants needed for explanations.

(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.

258
Ex—259

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

(5) Plants grow because they receive sunlight.

(6) Divorce is caused by marriage.

259
Ex—260

(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.

260
Ex—261

(10) What correlation is reported in the following, and what might be a common
cause for it?
"Our main finding was that people with a high frequency of religious
participation in young adulthood were 50 percent more likely to become obese
by middle age than those with no religious participation in young adulthood,"
says Matthew Feinstein, the study’s lead investigator and a fourth-year medical
student at Northwestern University Feinberg School of Medicine."
"And that is true even after we adjusted for variables like age, race, gender,
education, income, and baseline body mass index," he added.
The study, presented at a meeting of the American Heart Association,
followed 2,433 men and women starting between the ages of 20 and 32 for 18
years. Study subjects were all of normal weight at the beginning of the study. By
the end, however, those who had attended a religious function at least once a
week were more likely to be obese, posting a body mass index of 30 or higher.
(From "Praise the lard? Religion linked to obesity in young adults"
http://www.msnbc.msn.com/id/42256829/ns/health-diet_and_nutrition/ )

261
Ex—262

An Introduction To Reasoning
Exercise Set (1) on Mill's Methods (14.4-7)

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—263

(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—264

(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—265

An Introduction To Reasoning
Exercise Set (2) on Mill's Methods (14.4-7)

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—266

(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—267

(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.
Ex—268

(7) By 1955, the cholesterol-heart attack connection was attracting some respectability.
A study was done that measured cholesterol blood levels in people from seven
different countries. Citizens of Finland, who ate the most saturated fats, had an
average cholesterol reading of over 260 (mg/dL). The Japanese, who consumed the
least saturated fat, had average cholesterol readings of a little over 160. Over a 10-
year period, the number of fatal heart attacks per 1,000 men was about 70 in Finland
and a little less than 5 in Japan. Saturated fat made up 20% of the Finnish diet, but
only 2.5% of the Japanese diet.
(http://www.lef.org/magazine/mag2009/feb2009_The-Cholesterol-
Controversy_01.htm)
Ex—269

An Introduction To Reasoning
Exercise Set (1) on 4-Cell Tables (15.2)

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."    (

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 the method used to create the groups.
Ex—270

(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—271

(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—272

(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—273

An Introduction To Reasoning
Exercise Set (2) on 4-Cell Tables (15.2)

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—274

(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—275

(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
Ex—276

An Introduction To Reasoning
Exercise Set (1) on Necessary and Sufficient Conditions, INUS Conditions (15.3-4)

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:
Ex—277

Sufficient Condition:    Yes   No
Counterexample:
Ex—278

(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—279
Ex—280

An Introduction To Reasoning
Exercise Set (2) on Necessary and Sufficient Conditions, INUS Conditions (15.3-4)

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:
Ex—281

Sufficient Condition:    Yes   No
Counterexample:
Ex—282

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—283
Ex—284

Part 3

(10) Make a list of all of the explanatory factors (for the candidates' success)
http://www.miamiherald.com/2010/08/22/1786600/mccollum-meek-surge-
Ex—285

An Introduction To Reasoning
Exercise (1) on Experimental Methods (15.5-7)

(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—286

(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—287

An Introduction To Reasoning
Exercise (2) on Experimental Methods (15.5-7)

(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
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—288

(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—289

(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—290

An Introduction To Reasoning
Exercise Set (1) on Arguments Involving Explanations (16.1-4)

For each argument, (i) put the argument in standard form, including (as missing
premises, if necessary) the "additional" premises needed to make the inference 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—291

(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—292

(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—293

(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—294

(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—295

An Introduction To Reasoning
Exercise Set (2) on Arguments Involving Explanations (16.1-4)

For each argument, (i) put the argument in standard form, including (as missing
premises, if necessary) the "additional" premises needed to make the inference 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 inference 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—296

(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—297

(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—298

(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—299

(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

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