1. Thinking Mathematically
Logic
3.3 Truth Tables for Negation, Conjunction, and Disjunction

2. Definitions of Negation, Conjunction, and Disjunction
Negation ~: not
The negation of a statement has the opposite truth value from the statement.
2. Conjunction ^ : and
The only case in which a conjunction is true is when both component statements are true.
Disjunction: V : or
The only case in which a disjunction is false is when both component statements are false.

3. Examples: Negation, Conjunction, Disjunction
Exercise Set 3.3 #3, 7, 11
p: = 10
q: 5 x 8 = 80
What is the truth value of the following statements?
p ^ q
~p ^ ~q
p V ~q
What if you didn’t know the truth values of the component statements p and q. How could you view the truth value of the compound statement.

4. Truth Tables
A truth table list all possible truth values for a compound statement based on the truth values of its component (simple) statements
A complete truth table must have one row for each possible combination of truth values of its component statements.
If a compound statement has n component statements, then the complete truth table has 2n rows.

5. “Truth Tables” - Negation
If a statement is true then its negation is false and if the statement is false then its negation is true. This can be represented in the form of a table called a “truth table.”

6. Truth Tables -- Conjunction
A conjunction is true only when both simple statements are true.

7. Truth Tables -- Disjunction
A disjunction is false only when both component statements are false.

8. Examples Exercise Set 3.3 #21, #27, #31 Construct a truth table for
~(p V q)
~(~ p V q)
~ p V (p ^ ~q)

9. Thinking Mathematically
Logic
3.3 Truth Tables for Negation, Conjunction, and Disjunction