Prove each of the following. Be sure to indicate whether you are using a Direct Proof, a Contrapositive Proof, a Proof by Cases, or a Proof by Contradiction. If you use a Proof by Cases, be sure to indicate what each case is, and in each case, which type of proof you are using. (a) Prove that for an integer n, n 2 is even if and only if n is even. (b) Let a and b be integers and define c