Math Insight

Definition of superset


A set $A$ is a superset of another set $B$ if all elements of the set $B$ are elements of the set $A$. The superset relationship is denoted as $A \supset B$.

For example, if $A$ is the set $\{ \diamondsuit, \heartsuit, \clubsuit, \spadesuit \}$ and $B$ is the set $\{ \diamondsuit, \clubsuit, \spadesuit \}$, then $A \supset B$ but $B \not\supset A$. Since $A$ contains elements not in $B$, we can say that $A$ is a proper superset of $B$. Or if $I_1$ is the interval $[0,2]$ and $I_2$ is the interval $[0,1]$, then $I_1 \supset I_2$.