Exercise 65 Page 114

Let's begin by reviewing the concept of a conditional and its inverse.

Conditional	Inverse
$p\to q$	$\sim p\to \sim q$

We know that the hypothesis $p$ is $\text{true},$ and the conclusion $q$ is $\text{false}.$ To form the inverse, we negate both the hypothesis and the conclusion of the conditional. The negation of true is false, and the negation of false is true. Recall that when a hypothesis is false, the conditional will always be considered true, regardless of whether the conclusion is true or false. In this case, the hypothesis of the inverse is false, so we can conclude that the inverse of our statement is true.