1. Proofs Determine whether each statement is true or false. For each true statement, give a proof as justification. For each false statement, give a counterexample as justification. (a) If x and y are both even integers, then x * y is even. (b) If x e Z and y E Z and x > y, then x-y > 0. (c) If x and y are both even integers, the mean of the two numbers is odd. (d) If x and y are both even integers and x > y, then x*y is an even integer where x* y > y