What is the result of the union of an empty set with any set A?

The result of the union of an empty set with any set A is precisely set A itself. This is based on the fundamental properties of set operations, specifically the definition of the union.

The union of two sets is defined as the set containing all elements that are in either of the sets. When one of the sets is empty, it contributes no elements to the union. Therefore, the union simply consists of all the elements that are present in the other set, which in this case is set A.

For any set A, regardless of its contents, when you perform the union with the empty set, the outcome remains unchanged because the empty set does not add or remove any elements. This property remains true across all types of sets, reinforcing the fact that the empty set acts as a neutral element in the union operation.