1. How do I show that two compound propositions are logically equivalent?
Truth Tables
How do I show that two compound propositions are logically equivalent?

2. Creating Truth Tables
To create truth tables you start with the columns for the propositions p, q, and when needed, r.
Then you build the table to show the compound propositions
If the final column of the two tables are equivalent, then we say that the statements are logically equivalent

3. Create Truth tables for andp q p q T F T F T F F F F F T T F T F T F T T F T T T T
Because the last two columns are the same these compound propositions are logically equivalent

4. Example Two – DeMorgan Properties
Create and fill in the truth table for p q p q T F T F

5. YOU DO: Construct Truth tables for: and Are they logically equivalent?p q p q T F T F

6. YOU DO: Are the following compound propositions logically equivalent?

7. Construct a truth table forp q
What do you notice about the last column?
This is called a TAUTOLOGY – when the last column is all true T F

8. THREE PROPOSITIONS Construct the truth table for p q r T F T T T F T T

9. Construct a truth table for:p q r T F