2. Let A = {1,2,3,4}. Let F be the set of all functions from Ato A. Recall that IA ? F is the identity function on A given byIA(x) = x for all x ? A. Consider the function E : F ? A given byE(f) = f(1) for all f ? F.
(a) Is the function E one-to-one? Prove your answer.
(b) Is the function E onto? Prove your answer.
(c) How many functions f ? F are there so that E(f) = E(IA)?Explain.
(d) How many onto functions f ? F are there so that E(f) =E(IA)? Explain.
