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2) Write direct proofs for the following statements. All variables are integers unless mentioned otherwise. (a) The sum of two odd integers is even. (b) The product of two rational numbers is rational. (c) If 4n, then n is even. (d) If a is an even integer and b is an odd integer, then a2+b2+1 is an even integer. (e) Let a and b be integers. We say ab if ab=10k for some integer k. Prove that if ab and cd, then (ac)(bd)