a) Consider the following theorem: "if x and y are odd integers, then x + y is
even". Give a direct proof of this theorem
b) Consider the following theorem: "If x is an odd integer, then x + 2 is odd".
Give a proof by contraposition of this theorem
c) Consider the following theorem: "If n is an even integer, then n + 1 is odd".
Give a proof by contradiction of this theorem
d) Suppose you are allowed to give either a direct proof or a proof by
contraposition of the following: "if 3n + 5 is even, then n is odd". Which
type of proof would be easier to give? Prove and explain why.
