# Equivalence Relation

**DEFINITION1:** Let be a set and . If the relation is reflexive, symmetric and transitive, then the relation is called an "equivalence relation" and denoted by in general.

**DEFINITION2:** Let be an equivalence relation over a set and . The set defined as is called the “equivalence class” of under and denoted by , or . Since for every , then . So the equivalence class is non-empty for every . The family of all the equivalence classes of the relation is called the “quotient set” of by and denoted by

I.e.,

.

**DEFINITION3:** Let be an equivalence relation over a set and . If , then is called a “representative class” of the equivalence class .