a) Let C be a set, and A and B be disjoint sets. Find a bijection vh: CA × CB → CAUB¸ and show that it is well-defined, injective,and surjective.

(b) Denote by |X| the cardinality of a set X. (i) Let A, B, C, and D be sets such that |A| = |B| and |C| =|D]. Prove that |Ac| = |Bd (ii) Find a pair of sets A and B so that |A| < |B|, but |AN| =|B]. Find an example where B is countably infinite. (Noproof is necessary.) (iii) Find two different explicit bijections f, g: 5N → 2N. By explicit, I mean recipes for converting elements of 5N into elements of 2N. Explain your answer graphically in terms of the trees for 2N and 5N.