What is the result of the intersection between an empty set and a set with n elements?

The intersection between two sets consists of the elements that are common to both sets. When one of the sets is empty, it contains no elements at all. Regardless of the number of elements in the other set, the intersection will also have no elements because there are no elements in the empty set to match with those in the set that contains n elements. Therefore, the result of the intersection of an empty set with any other set, whether it has one element, multiple elements, or even an infinite number of elements, will always be an empty set.

This property of sets is fundamental in set theory, reinforcing the understanding that an empty set does not contribute any elements to intersections. Consequently, the intersection is defined as containing no elements, affirming that it remains an empty set.