contrapositive

"If you are wearing a hat, you are a baseball fan." and "If you are not a baseball fan, you are not wearing a hat." It's called a contrapositive. definition: : a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given...

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 +...