which of the following is also a secure PRG?

Problem 7. Given G as a secure PRG which of the following is also a secure PRG? Give a high level idea of the proof for your answer for each item: a) G ($1||$2) :=G()G(82) where A denotes bit-wise AND and || is concatenation. b) G2(81||$2) :=G(81) e G(82). c) G3(s) := G(8) 1" (XOR n-th bit with 1) d) G4(8)=G(s)[0,..., N - 1) (select first n - 1 bits). e) G5(s) := (G(s), G(s)). f) G&($1||$2) := ($1,G($2)). Problem 7. Given G as a secure PRG which of the following is also a secure PRG? Give a high level idea of the proof for your answer for each item: a) G ($1||$2) :=G()G(82) where A denotes bit-wise AND and || is concatenation. b) G2(81||$2) :=G(81) e G(82). c) G3(s) := G(8) 1" (XOR n-th bit with 1) d) G4(8)=G(s)[0,..., N - 1) (select first n - 1 bits). e) G5(s) := (G(s), G(s)). f) G&($1||$2) := ($1,G($2))