5. (a) Give a direct proof of: If x is an odd integer and y is an even integer, then x + y is odd. (b) Give a proof by contradiction of: If n is an odd integer, then n2 is odd. (c) Give an indirect proof of: "If x is an odd integer, then x + 2 is odd. (d) Use a proof by cases to show that there are no solutions in positive integers to the equation x4 + y4 = 100. (e) Prove that given a nonnegative integer n, there is a unique nonnegative integer m, such that m s n