Let G be a pseudorandom generator that on security paramter n > 1, takes as input bitstrings of length n and has expansion factor 1(n) 2n. In each of the following cases, say whether G, is necessarily a pseudorandom generator. If yes, give a proof; if not, show a counterexample. (a) Define G,(s) G(81, . . . , srn/21), where s = 81, . . . , sn (b) Define G,(s)=G(08111s). (c) Define G,(s) = G(rotate(s, 1)), where rotate(s, 1) rotates the bits of s to the right by one position