Solution
= Solution
The <conjugacy class> of $g$ is
$$
\boxed{\operatorname{Cl}_G(g)=\{hgh^{-1}:h\in G\}.}
$$
If $N$ is a <normal subgroup> and $g\in N$, then normality gives $hgh^{-1}\in N$ for every $h$. Thus the whole conjugacy class of each member of $N$ is contained in $N$, and
$$
\boxed{N=\bigcup_{g\in N}\operatorname{Cl}_G(g).}
$$
Conjugacy classes partition the group, so this is a union of complete disjoint classes, never selected fractions of classes.