4.* (a) Let S = {1, 2, 3, 4}. Define F: SN by F(x) = x² for each x = S. What is the range of the function F and what is F(S)? How do these two sets compare? Now let A and B be sets and let f: A B be an arbitrary function from A to B. (b) Explain why f(A) = range(f). (c) Define a function g: A f(A) by g(x) = f(x) for all x in A. Prove that the function g is a surjection.

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