A subset of a set S (on which an equivalence relation is defined) that consists of all the elements of S that are equivalent to each other, and to no other elements of S. An equivalence relation provides a partitioning (see covering) of a set into a number of mutually disjoint equivalence classes.

The relationship ‘has the same surname as’ defined on the set of people produces an equivalence class consisting of all those with Jones as surname, another consisting of those with Smith as surname, and so on.