A proper superset of a set `A` is a superset of `A` that is not equal to `A`. In other words, if `B` is a proper superset of `A`, then all elements of `A` are in `B` but `B` contains at least one element that is not in `A`.

For example, if `A =\{1,3,5\}` then `B=\{1,3,4,5\}` is a proper superset of `A`. The set `C=\{1,3,5\}` is a superset of `A`, but it is not a proper superset of `A` since `C=A`. The set `D=\{1,3, 7\}` is not even a superset of `A`, since `D` does not contain the element 5.

See also proper subset.