2. Proof by contradiction: (a) Let a and b be integers. Show that if a²b -a is even, then a is even or b is odd. (b) Let G be a simple graph on n ≥ 4 vertices. Prove that if the shortest cycle in G has length 4, then G contains at most one vertex of degree n - 1. (c) Let x be a rational number and let y be an irrational number. Show that if x(y rational, then x = 0. -1) is

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