set complement and superset
I'm not sure what you mean by "a set complement of&nbsp;$S$."

If you mean to allow complements with respect to different universal sets, then the statement in the question is not true. For example, let $S=\{1\}$. Its complement&nbsp;$S'$ with respect to $\{1,2\}$ is&nbsp;$\{2\}$. $\{1,2\}$ is a superset of&nbsp;$S'$ but its set complement with respect to $\{1,2,3\}$ is&nbsp;$\{3\}$, which is not a subset of $S=\{1\}$.

On the other hand, if you mean "the set complement of&nbsp;$S$" with respect to some fixed universal set&nbsp;$U$,the statement is true. We have $S'=U\setminus S$ and choose some $T \supseteq S'$. Then $U\setminus T \subseteq U\setminus S' = S$.