An equivalence class is defined as a subset of the form {x element X:x R a}, where a is an element of X and the notation "x R y" is used to mean that there is an equivalence relation between x and y. It can be shown that any two equivalence classes are either equal or disjoint, hence the collection of equivalence classes forms a partition of X. For all a, b element X, we have a R b iff a and b belong to the same equivalence class. A set of class representatives is a subset of X which contains exactly one element from each equivalence class.

congruence | coset | equivalence relation