Definition
A given binary relation ~ on a set A is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive. Equivalently, for all a, b and c in A:
- a ~ a. (Reflexivity)
- if a ~ b then b ~ a. (Symmetry)
- if a ~ b and b ~ c then a ~ c. (Transitivity)
A together with the relation ~ is called a setoid. The equivalence class of a under ~, denoted, is defined as .
Read more about this topic: Equivalence Relation
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