(a) Use a proof by contraposition to show that if x + y 2, where x and y are real numbers, then x 1 or y 1. (b) Prove that if n is an integer and 3n+2 is even, then n is even using (1) a proof by contraposition, and (2) a proof by contradiction. (c) Prove the triangle inequality, which states that if x and y are real numbers, then |x|+|y||x+y| (where |x| represents the absolute value of x, which equals x if x 0 and equals x if x < 0).