# Logic Homework

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```					                                Logic Homework
April 5, 2010
Name:______________________

To do proofs well, one must understand the logic behind proofs. Let’s start with some
basic logic terms.

Original Statement:
If p, then q.
p is called the “hypothesis” and q is called the “conclusion”.
Ex. If it is Valentine’s Day, then I am going on a date.

Converse:
If q, then p.
Ex. If I am going on a date, then it is Valentine’s Day.
Not true, in general

Inverse:
If not p, then not q.
Ex. If it is not Valentine’s Day, then I am not going on a date.
Not true, in general

Contrapositive:
If not q, then not p.
Ex. If I am not going on a date, then it is not Valentine’s Day.
True, in general. Logically equivalent to the Original Statement.

Directions: For the following statements, first rewrite the statement as an “If-Then”
statement, and then write the Converse, Inverse, and Contrapositive of each statement.

1. “If you like it, then you should have put a ring on it.” – Beyonce
2. “If you see us in the club, then we’ll be actin’ real nice” – Nelly Furtado and
Justin Timberlake

3. No parking here, violators will be towed.

4. All of my students are smart.
5. “My anaconda don’t want none unless you’ve got buns, hun.” – Sir Mix-a-Lot

A Syllogism is a logical argument that is inferred from two or more propositions.

Ex.      (1) I only bike in the summer.
(2) I am biking.
(3) Conclusion: It is summer.

Ex.     (1) No reptiles have fur.
(2) All snakes are reptiles.
(3) No snakes have fur.
Directions: From each statement, either form a syllogism or identify the parts of a
syllogism.

1. “Yes just to know know know her, is to love love love her, and I do, and I do, and
I do. And I do, and I do, and I do.” – The Beatles
2.    “If you feelin’ like a pimp, go and brush your shoulders off. Ladies is pimps too,
go and brush your shoulders off.” – Jay-Z

3. “She was supposed to buy you shorty TYCO with your money. She went to the
doctor got lypo with your money.” – Kanye West

4. “Yeah you’ve got that something, I think you’ll understand. When I feel that
something, I wanna hold your hand.” – The Beatles
5. “I wish I was a little bit taller, I wish I was a baller, I wish I had a girl who looked
good I would call her.” – Skee-Lo

6. “If I got me a wealthy man ,I wouldn't have to work at all, I'd fool around and
have a ball... Money, money, money” – Abba

7. “If I Had \$1000000, We wouldn't have to eat Kraft Dinner. (But we would eat
Kraft Dinner. Of course we would, we'd just eat more. And buy really expensive
ketchup with it. That's right, all the fanciest Dijon Ketchup. Mmmmmm.)” –
Math

Directions: For 1-4, construct the original statement, converse, inverse, and
contrapositive. State which of these are true. For 4-6, use 1-3 to complete the syllogisms
given the part (1), (2) or (3).

1. Parallel lines never intersect.

2. The angle measures of a triangle sum to 180 degrees.

3. All parallelograms have two opposite pairs of parallel lines.
4. (1) This figure is constructed from two pairs of nonintersecting lines.

(2)

(3)

5. (1) This figure can be subdivided into two triangles.

(2)

(3) The angle measures of this figure sum to ________ degrees

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