20 points) Suppose that you have two efficiently computable functions G1,G2, both with xpansion (n)=3n; that is G1,G2:{0,1}n{0,1}3n, and you know that at least one of nem is a PRG. From these two functions, you want to construct a new function that is uaranteed to be a PRG. a) Consider the function G(s)=G1(s)G2(s). Is G guaranteed to be a PRG? If so, prove it. If not, give a counterexample. ) Consider the function G(s1s2)=G1(s1)[1:3n/2]G2(s2)[3n/2+1:3n]. That is, we concatenate the first 3n/2 bits of of G1(s1), with the last 3n/2 bits of G2(s2). Is G guaranteed to be a PRG? If so, prove it. If not, give a counterexample. (For this part, assume that n is even.) c) Construct your own new PRG G:{0,1}2n{0,1}3n which utilizes both G1 and G2. You should not disregard one of the G1,G2, as you also do not know which one is a valid PRG, and you should prove that your construction satisfies the definition from lecture