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An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.
The empty set is the set that contains no elements. (It is the empty set, not an empty set, because there is only one of them. It is a unique mathematical object.)
It depends on what it contains: none, if it is empty!It depends on what it contains: none, if it is empty!It depends on what it contains: none, if it is empty!It depends on what it contains: none, if it is empty!
The empty element is a subset of any set--the empty set is even a subset of itself. But it is not an element of every set; in particular, the empty set cannot be an element of itself because the empty set has no elements.