Let $N$ be a normal subgroup of a group $G$ such that $N\cap G'=\{e\}$, where $G'$ is the derived/commutator subgroup of $G$. Then
i.) $N\subseteq Z(G)$, where $Z(G)$ is the center of $G$
ii.) $Z(G/N)=Z(G)/N$
Help me figure this out please... Thank you..