Problem 2: Consider the set of integers. 1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the product of two odd integers is odd. 3. Prove that if n is an integer and n + 5 is odd, then n is even using a) A proof by contraposition. b) A proof by contradiction. 4. Prove or disprove that if m and n are integers such that mn = 1, then either m = 1 and n 1, or else m=-1 and n = -1. 5. Prove that these four statements about the integer n are equivalent: a) n is odd. b) 1 - n is even. c) nis odd. d) n + 1 is even. 6. Prove that if m and n are integers and mn is even, then m is even or n is even. 1