1. The Lost Art of Argument
Logic
The Lost Art of Argument

2. Propositions
Definition: Proposition – A statement that is either true or false (but not both).
Examples:
This shirt is red
√2 is irrational
1 + 1 = 5
There are more stars than grains of sand

3. Propositions
Definition: Proposition – A statement that is either true or false (but not both).
Not Propositions:
x + 2 = 17
When is Thanksgiving?
Why are these not propositions?

4. Propositions Definition: Conjunction – P Λ Q (“P and Q”) Example:
P = Three quarters equal one dollar
Q = 8 is an even number
P Λ Q = Three quarters equal one dollar and 8 is an even number

5. Propositions Definition: Disjunction – P ν Q (“P or Q”) Example:
P = Three quarters equal one dollar
Q = 8 is an even number
P Λ Q = Three quarters equal one dollar or 8 is an even number

6. Propositions Definition: Negation - ~P (Not P) Examples:
P = Three quarters equal one dollar
Q = 8 is an even number
~P = It is not the case that three quarters equal one dollar
or: Three quarters do not equal one dollar
~Q = It is not the case that 8 is an even number
or: 8 is not an even number

7. Truth Tables P Q (P Λ Q) True False
Truth tables are a way to visually organize whether a statement is true or false.
This is the truth table for: P Λ Q P Q
(P Λ Q)
True
False

8. Truth Tables P Q (P ν Q) True False
Truth tables are a way to visually organize whether a statement is true or false.
This is the truth table for: P ν Q P Q
(P ν Q)
True
False

9. Truth Tables
Definition: Equivalent – Two propositions are equivalent when their truth values are the same.
Here are two truth tables. Are the two propositions, ~(P Λ Q) and (~P v ~Q) equivalent? P Q
(P Λ Q)
~(P Λ Q) T F P Q ~P ~Q
(~P v ~Q) T F

11. Logic Worksheet
1. Place a check next to all statements that are propositions.
a. ____ The National debt of Poland is more than $30 Billion.
b. ____ Where is my book?
c. ____ x + 3 = 0
d. ____ Albert Einstein never wore red boots.
e. ____ Horses have gills.
f. ____ x^2 ≥ 0

12. Logic Worksheet 2a. Construct a proposition that is false.
2b. Write the negation of the proposition.
2c. Is the negation of the false proposition true or false?
2d, Will the negation of a false proposition always be true?

13. Logic Worksheet 3. Construct truth tables for ~(P V Q) and ~P ^ ~Q
Are the propositions ~(P V Q) and ~(P V Q) equivalent? Why? P Q
(P V Q)
~(P V Q) T F P Q ~P ~Q
~P ^ ~Q T F

15. Logic - Review
Proposition – A statement that is either true or false (but not both)
Conjunction – And
Disjunction – Or
Negation – Not
Truth Tables can be used to determine Equivalence
Equivalence – Two propositions have the same truth values