\begin{definition}[Definition:Cover of Set/Subset]
Let $S$ be a set.
Let $T \subseteq S$ be a subset.
Let $\CC$ be a set of subsets of $S$.
Then $\CC$ is a '''cover of $T$''' {{iff}} $T \subseteq \ds \bigcup \CC$, where $\cup$ denotes union.
\end{definition}