Various binary operations on sets

The various binary operations on sets are as follows:

Union: Union of the sets A and B, denoted A ∪ B, is the set of all objects that are a member of A, or B, or both. The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4}.

Intersection: Intersection of the sets A and B, denoted A ∩ B, is the set of all objects that are members of both A and B. The intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3}.

Complement: Complement of set A relative to set U, denoted Ac, is the set of all members of U that are not members of A. This terminology is most commonly employed when U is a universal set, as in the study of Venn diagrams. This operation is also called the set difference of U and A, denoted U \ A. The complement of {1,2,3} relative to {2,3,4} is {4} , while, conversely, the complement of {2,3,4} relative to {1,2,3} is {1}.

Difference: Symmetric difference of sets A and B is the set of all objects that are a member of exactly one of A and B (elements which are in one of the sets, but not in both). For instance, for the sets {1,2,3} and {2,3,4} , the symmetric difference set is {1,4} . It is the set difference of the union and the intersection, (A ∪ B) \ (A ∩ B).

Cartesian Product: Cartesian product of A and B, denoted A × B, is the set whose members are all possible ordered pairs (a,b) where a is a member of A and b is a member of B.