Consider for example problem 30: Statement: ∀ integers a, b, and c, if a − b is even and b − c is even, then a − c is even. Inverse: ∀ integers a, b, and c, if a − b is not even or b − c is not even, then a − c is not even. The statement is true, but its inverse is false. As a counterexample, let a = 3, b = 2, and c = 1. Then a-b=1, which is not even. But a-c=2 is even. Hence the inverse is false.
Work Step by Step
Recall that two statement forms are logically equivalent if, and only if, they have identical truth values for each possible substitution of statements for their statement variables.