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Question B 6 (a) Consider sets X, Y, Z and functions f : X - Z and g : Y - Z. Define the set X xjaY = {(r, y)|re X and y E Y for which / (x) = g(y)}: [12 marks] (i) Suppose that |Z| = 1, a singleton set. What is another name for X xy Y? (1 mark) (ii) Suppose that |Z) = 1. How many subsets are there of X x/, Y? (2 marks) (ii) Suppose that |Z] = 1. How many relations are there on X x/ Y? (2 marks) (iv) Suppose that 2 = {0, 1} and let id: 2 - 2 denote the identity function. Prove that there is a bijective function from 2 x id id 2 to 2