Let $G$ be a PRG$.$ In each of the following, say whether $G^{\text{'}}$ is necessarily a PRG$.$ If yes, give a

proof. If not, show a counterexample.

$($a$)G^{\text{'}}(s)=s$

$($b$)G^{\text{'}}(s)=G(\frac{?}{\text{b}\text{a}\text{r}}(s)),$ where $\frac{?}{\text{b}\text{a}\text{r}}(s)$ denotes $s$ with each bit flipped.

$($c$)G^{\text{'}}(s)\frac{?}{b}=ar(G(s))$

$($d$)G^{\text{'}}(s)=G(0^{|s|}||s),$ where $|s|$ is the length of $s$