a) Consider the following theorem: "ifx and y are odd integers, then x+y is b) Consider the following theorem: "Ifx is an odd integer, then x +2 is odd c) Consider the following theorem: "If n is an even integer, then n 1 is odd" d) Suppose you are allowed to give either a direct proof or a proof by even". Give a direct proof of this theorem Give a proof by contraposition of this theorem Give a proof by contradiction of this theorem contraposition of the following: "if3n 5 is even, then n is odd". Which type of proof would be easier to give? Prove and explain why