Set theory

A set is a collection of distinct objects, considered as an object in its own right. For example, A = {1, 2, 3} is a set.

The intersection of two sets A and B, denoted A ∩ B, is the set of elements that are common to both A and B.

A ∩ B = {2, 3}.

The union of two sets A and B, denoted A ∪ B, is the set of all elements that are in A, in B, or in both.

A ∪ B = {1, 2, 3}.

The complement of a set A, denoted A', is the set of all elements in the universal set that are not in A.

A' = {1, 4, 5}.

Roster form is a way of specifying a set by listing its elements within curly braces. For example, A = {1, 2, 3}.

Set-builder notation is a shorthand used to describe a set by stating the properties that its members must satisfy. For example, A = {x | x is an even number}.

Two sets are equivalent if they have the same number of elements, regardless of whether the elements are the same.