Complete both of the following points. (a) Prove that every PRG is also a OWF. Specifically, suppose G : {0, 1}^n {0, 1}^m for m > n is a PRG, prove G is also a OWF. (b) Prove now that not every OWF with m > n is a PRG. Specifically, let f : {0, 1}^n {0, 1}^m with m > n be a OWF. Use f to build another function f : {0,1}^n {0,1}^m+1which is a OWF but which is not a PRG. Prove that f is a OWF (assuming f is) but is not a PRG. (c) Suppose (Gen, Enc, Dec) is a PKE scheme. Recall that we normally model the key genera- tion procedure Gen() as a randomized procedure which takes no input and which outputs a key pair (pk, sk). Let us instead for this problem be explicit about the randomness used by Gen. So we will think of Gen() as a deterministic function which takes as input a random string r {0, 1}^k and outputs (pk, sk). Prove that when modeled this way, Gen is a OWF.