Let G be a pseudorandom generator with expansion factor `(n) > 2n. In each of the following cases, say whether G0 is necessarily a pseudorandom generator. If yes, give a proof; if not, show a counterexample.

eb, output of the experiment is defined to be I b and 0 otherwise. Provide a definition of a pseudorandom generator based on this exper- iment, and prove that your definition is equivalent to Definition 3.14. (That is, show that G satisfies your definition if and only if it satisfies Definition 3.14.) 3.6 Let G be a pseudorandom generator with expansion factor l(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) def G($1.--8[n/2]), where s = $1.-Sn. (b) Define G'(8) def G (Ols|||s). (c) Define G' (s) de G(s) || G(s +1). def