### Definition of union

The union of a set $A$ with a $B$ is the set of elements that are in either set $A$ or $B$. The union is denoted as $A \cup B$.

For example, if $A$ is the set $\{ \diamondsuit, \heartsuit, \clubsuit, \spadesuit \}$ and $B$ is the set $\{ \triangle, \heartsuit, \spadesuit \}$, then $A \cup B = \{ \diamondsuit,\heartsuit, \clubsuit, \spadesuit, \triangle \}$. Or if $I_1$ is the interval $[0,2]$ and $I_2$ is the interval $[1,3]$, then $I_1 cup I_2 = [0,3]$.