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 24 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 a be a rational number and let y be an irrational number. Show that if a(y-1) is rational, then a = 0.