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