1. Truth Tables for the Conditional and Biconditional
3.3
Truth Tables for the Conditional and Biconditional

2. Conditional
The conditional statement p g q is true in every case except when p is a true statement and q is a false statement. T F
Case 4
Case 3
Case 2
Case 1 q p

3. Biconditional
The biconditional statement, p↔q means that p g q and q g p or, symbolically (p g q) ^ (q g p). p ↔ q T F
Only true when both results are the same

5. Example: Truth Table with a Conditional
Construct a truth table for ~p g ~q.
Solution: Construct standard four case truth table.
Then fill-in the table in order, as follows: p q ~p g ~q T F T F F T T F F T 1 3 2
It’s a conditional, the answer lies under the g.

6. Solve ~Q ~P

7. Self-Contradiction
A self-contradiction is a compound statement that is always false.
When every truth value in the answer column of the truth table is false, then the statement is a self-contradiction.

8. Tautology A tautology is a compound statement that is always true.
When every truth value in the answer column of the truth table is true, the statement is a tautology.

9. Implication
An implication is a conditional statement that is a tautology.
The consequent will be true whenever the antecedent is true.

10. If p is true, q is false and r is false, find the truth value of the statement
~[ (~p V q) (r ^ q) ]

11. Homework
P. 124 # 1 – 6, 9 – 72 (x 3)
Ch quiz next class