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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.

Author: Wolfgang Schreiner
Last Modification: January 12, 2000

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