A set is a collection of individual elements in the domain . The universal set contains every element in . The null set contains no element.


If is a set in the domain , must be a subset of the universal set , denoted as .


If consists of some but not all elements, is then called a proper subset of , denoted as .
Unions, Intersections, Complements

The definition of union ("or"), intersection ("and"), and complement ("not") can be illustrated by Venn Diagrams as follows:

Suppose that A and B are two sets in the same domain whose universal set is .


The union of A and B consists of all elements which belong to either A or B, denoted by .


The intersection of A and B consists of only elements which belong to both A and B, denoted by .


The complement of A consists of elements which do not belong to A, denoted by .

Important Properties

Distributive Laws

De Morgan's Laws