Look at the Contrapositive: If n is even, then 3n + 2 is even... Suppose that the conclusion is false, i.e., that n is even. Then n = 2k for some integer k. Then we have: 3n + 2 = 3(2k) + 2 3n + 2 = 6k + 2 3n + 2 = 2(3k + 1). Thus 3n + 2 is even, because it equals 2j for an integer j = 3k + 1. So 3n + 2 is not odd. We have shown that ¬(n is odd) → ¬(3n + 2 is odd), therefore, the contrapositive (3n + 2 is odd) → (n is odd) is also true.
