Set theory is a branch of mathematical logic. Though set theory is usually applied in mathematics, the theory can also be used in other fields. The modern study of set theory was developed in the 1870s.

Set theory expresses a binary relation between an object and a set. Every object of a set is a member or an element. Sets are also objects and can belong to other sets.

A binary relation between two sets is the subset relation, which is also called set inclusion. If all the members of set A are also members of set B, then A is a subset of B. To give a more concrete example, we can say that the members of set A are puppies and the members of set B are dogs. Thus we can express the relation between the two sets by stating that the set of puppies is a subset of the set of dogs.

Numbers are common in set theory. The union of the sets X and Y is the set of all objects that are members of X, Y or both. The union of {1,2} and {2,3} is the set {1,2,3}. The intersection of the sets X and Y is the set of all objects that are members of both sets. The intersection of {1,2} and {2,3} is {2}.

A Venn diagram is a diagram that shows all the possible logical relations between different sets. The diagram usually consists of overlapping circles representing a set. The Venn diagram was conceived by John Venn around 1880. It is used to teach elementary set theory as well as illustrate simple set relationships.

Set theory is common in mathematics, but can also be applied to other areas such as computer science, linguistics and statistics. In set theory the relation between objects and sets and also between sets and other sets is clearly illustrated. Venn diagrams can be used to express all possible relations between sets.