Equivalence Relation
A relation is an equivalence relation when it is reflexive, symmetric and transitive, usually written .
Definition 2.30 (Equivalence Relation)
A relation is an equivalence relation if it is reflexive, symmetric and transitive.
We usually write for the case where and is an equivalence relation.
Examples
Relating two students when they were born in the same month is an equivalence relation, and it divides the set of students into subsets consisting of related elements. Among relations on , sharing the same final digit is an equivalence relation. On , defining when also yields an equivalence relation.
Related
Stated in
- Definition 2.30 (Equivalence Relation)§2.3 Relations