Problem 3 (12 marks) Let S be a set. a) Show that for any set T and any function f : T, the relation RpCS5x 5, defined as: (s,5) Ry if and only if f(s) = f[s'} is an equivalence relation. &3 b) Show that if R C S x 5 is an equivalence relation, then there exists a set T and a function fr 5 = T such that: (s,s") R if and only if fr(s) = fr(s') Problem 4 {5 marks) Show that for any sets A, B, C there is a bijection between A'*C) and {AF)C. o