Problem 6: Proofs (30 points) (a) Use a proof by contraposition to show that if ty22, where r and y are real numbers, then r 21 ory21. (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 z and y are real num bers, then Izl + ly| Iz+ equals if 0 and equals - ifx