Prove each of the following. please indicate which proof you are using

4. 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, n2 is even if and only if n is even. (b) Let a and b be integers and define c = a +b. Prove that c is even if and only if a and b have the same parity. (c) Prove that if z can be written as z = 2 . (an odd integer), then zx2-y, where x and y are integers. Hint: You will need to use the results of parts a and b