### Definition of intersection

The intersection of a set $A$ with a $B$ is the set of elements that are in both set $A$ and $B$. The intersection is denoted as $A \cap B$.

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