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Equivalence Relation

Definition: Let R be a binary relation on S. R is an equivalence relation on S, if it is reflexive, symmetric, and transitive on S:

R is equivalence relation on S: <=>

R subset S x S /\

R is reflexive on S /\

R is symmetric on S /\

R is transitive on S.

Many (not all) properties of the equality relation on S.