The Empty Set Has Only One Subset

The empty set (∅) is a set with no elements and is a subset of every set. In particular, it is also a subset of itself.

By definition, a set $A$ is a subset of another set $B$ if all elements of $A$ are also elements of $B$. Since the empty set has no elements, this condition is always satisfied for any set. Therefore, the empty set is a subset of itself.

However, the empty set cannot have any subset other than itself. To be a subset of the empty set, a set must contain only elements that are in the empty set—but there are no such elements. Thus, the empty set has exactly one subset: itself.