$3\mathrm{.}6$ Let $G$ be a pseudorandom generator. In each of the following cases, say whether $G^{\text{'}}$ is necessarily a pseudorandom generator. If yes, give a proof; if not, show a counterexample.

$($a$)$ Define $G^{\text{'}}(s)={?}^{\text{d}\text{e}\text{f}}G(\frac{?}{\text{b}\text{a}\text{r}}(s)),$ where $\frac{?}{\text{b}\text{a}\text{r}}(s)$ is the complement of $s.$

$($b$)$ Define $G^{\text{'}}(s)={?}^{\text{d}\text{e}\text{f}}\frac{T}{G(s)}.$

$($c$)$ Define $G^{\text{'}}(s)={?}^{\text{d}\text{e}\text{f}}G(0^{|s|}||s).$

$($d$)$ Define $G^{\text{'}}(s)={?}^{\text{d}\text{e}\text{f}}G(s)||G(s+1).$