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 counter example.

Define $G^{\text{'}}(s)$:$=G(s)$ where $s$ is the complement of $s.$

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

Define $G^{\text{'}}(s)$:$=G(0^{|s|}||s)$

Define $G^{\text{'}}(s)$:$=G(s)||G(s+1)$