1. (40 marks) Prove the following statements. Explicitly state the type of proof you are using and clearly describe each step of the proof. (a) (5 marks) If x and y are both odd integers, then x+y is an even integer. (b) (5 marks) If x and y are positive, even integers, then x x y is divisible by 4. (c) (10 marks) (x mod 2) x (y mod 2) (x x y) mod 2, where the mod operator gives you the remainder of the division (e.g. 3 mod 2 - 1)