Is the empty set a subset of the empty set?

Yes, the empty set is a subset of the empty set.

By definition, a set A is a subset of another set B if every element of A is also an element of B. The empty set, denoted as {} or , has no elements. Therefore, the condition of having all elements of the empty set also being elements of the empty set is trivially satisfied since there are no elements to consider.

This can be considered as an application of the concept of vacuous truth in logic, where a statement about all members of an empty set is considered true because there are no counterexamples. Consequently, we can conclude that the empty set is indeed a subset of itself.

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