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`.