Math Insight

Definition of subset


A set `A` is a subset of another set `B` if all elements of the set `A` are elements of the set `B`. In other words, the set `A` is contained inside the set `B`. The subset relationship is denoted as `A \subset B`.

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