Problem 3. Given a set S, define the function fs: P(S) P(S) such that for each ACS, fs(A) = S \ A. (a) Use the definition from lecture to argue that fs is injective. (You will not get credit for saying that injectivity is a consequence of the invertibility of fs.) (b) Use the definition from lecture to argue that fs is surjective. (You will not get credit for saying that surjectivity is a consequence of the invertibility of fs.)