# Definition:Cover of Set/Subset

## Definition

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 $T$ if and only if $T \subseteq \ds \bigcup \CC$, where $\cup$ denotes union.

## Illustration

The following diagram illustrates a cover of a subset $T$ of a set $S$: