1. (40 marks) Prove the following statements. Explicitly state the type of proof you are using and clearly describe each step of the proof. (d) (5 marks) For any integers, x and y, x + y 27 implies that x 2 4 or y 2 4 (e) (5 marks) For every integer n, n2 n is even. (f) (10 marks) If x is a rational number and y is an irrational number, then the sum of x and y is irrational