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Definition

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 and are two sets in the same domain whose universal set is .

 • The union of and consists of all elements which belong to either or , denoted by . • The intersection of and consists of only elements which belong to both and , denoted by . • The complement of consists of elements which do not belong to , denoted by .

 Important Properties Distributive Laws De Morgan's Laws