Suppose $S$ and $T$ are sets. Then the union of $S$ and $T$, denoted $S\cup T$, is the set whose elements are those that are elements of $S$ or of $T$, or both. More formally, \begin{align*} x\in S\cup T\text{ if and only if }x\in S\text{ or }x\in T \end{align*}