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

Warm Up 11/4/10 Write the following statements in symbols: p: It is snowing q: It is the month of January It is not snowing and it is March It is snowing and it is the month of January It is the month of January only if it is snowing. It is snowing or it is January.

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

Create Truth tables for and p 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

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

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

YOU DO: Are the following compound propositions logically equivalent?

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

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

Construct a truth table for: p q r T F