Set Theory - Operations

In addition to the general properties of sets, there are three important set operations, they are union, intersection, and difference. The union of two sets S and T, written S∪T, is defined as the collection of those elements that belong to either S or T or both. The union of two sets corresponds to their sum.

The intersection of the sets S and T is defined as the collection of elements that belong to both S and T, and is written S∩T. The intersection of two sets corresponds to the set of elements they have in common, or in some sense to their product.

The difference between two sets, written S-T, is the set of elements that are contained in S but not contained in T.

If S is a subset of T, then S-T = 0, and if the intersection of S and T (S∩T) is the null set, then S-T = S.