set complement and superset If 'S is a set complement of S, then a set complement of a superset of S' is a subset of S.

Just want to verify that above is true just based on the definition of 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 $U\setminus T \subseteq U\setminus S' = S$.