a) Use the method of direct proof to prove the following statements. i. Prove that the product of two integers, one of the forms 5k1 + 1 and the other of the form 5k; + 1. where k1 and k2 are integers, is of the form 5"; + 1 for some integer k3. (3 Marks) ii. Suppose p,q E Z. pr|q then p2|q2. (3 Marks) b) Use the method of proof by contradiction to prove the following statements. i. For all real numbers x and y. if x + y 2 2, then either x 2 1 or y 2 1. (3 Marks) ii. Prove that J? is irrational