There are several basic set operations, the most common being the intersection of sets, union of sets, and the complement of sets. The following lists these operations (note: the first two operations obey the associative and communtative laws, and together they obey the distributive law):

Intersection—The intersection of two sets is the set of elements common to the two sets. For example, the intersection of sets A and B is the set of elements common to both A ∩ B. This is usually written as A D B. Thus, if A = {1, 2, 3, 4} and B = {3, 4, 5}, then the intersection of A and B would be {3, 4}.

Union—The union of sets is the combining of members of the sets. For example, the union of two sets A and B is the set obtained by combining members of sets A and B. This is usually written as A ∪ B. Thus, if A = {1, 2, 3, 4} and B = {3, 4, 5}, then the union of A and B would be {1, 2, 3, 4, 5}.

Complement or complementation—When the set of all elements under consideration must be specified, it is called the universal set. And if the universal set is U = {1, 2, 3, 4, 5} and A = {1, 2, 3}, then the complement of A (or A’) is the set of all elements in the universal set that are not A, or {4, 5}. The intersection between a set and its complement is the empty or null set (∅); the union of a set and its complement is the universal set.