Page "Equivalence class" Paragraph 14

Every element of is a member of the equivalence class.

Every two equivalence classes and are either equal or disjoint.

Therefore, the set of all equivalence classes of forms a partition of: every element of belongs to one and only one equivalence class.

Conversely every partition of comes from an equivalence relation in this way, according to which if and only if and belong to the same set of the partition.