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In this question, X and Y denote non-empty sets and Y is the set of all functions from X to Y. (a) Suppose that both X and Y are finite. Show that Y is finite as well. [4 marks] (b) Suppose that X is finite and that Y is countably infinite. Show that Y is countably infinite. [6 marks] (c) Let Y be a two-element set, which we just write as Y = 2. Determine, for any set X, the cardinality of 2 . Justify your answer! [5 marks] (d) Under what exact conditions are the sets X and YX equinumerous? Justify your answer! [6 marks] (e) State what it means that the set Y is dominated by X and show that, if there exists g E Y which is surjective, then Y is dominated by X. [4 marks]