Introducing the Contrapositive and Converse

Abstract

In the last chapter (see Theorem 2.7) we saw that two statement forms, P and Q, that have the same truth table are equivalent. This was also expressed by showing that the equivalence, P↔Q, is a tautology. When you are confronted with a mathematical statement that you need to prove, you will often find it helpful to paraphrase it. You will use tautologies to do so, since you don’t want to change the truth value of your statement. Some useful tautologies appeared in Theorem 2.9. More appear below and throughout this chapter.