# equivalence relation definition, equivalence relation meaning | English dictionary

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## equivalence relation

n     (Logic, maths)   a relation that is reflexive, symmetric, and transitive: it imposes a partition on its domain of definition so that two elements belong to the same subset if and only if the relation holds between them
English Collins Dictionary - English Definition & Thesaurus
equivalence   , equivalency
n
1    the state of being equivalent or interchangeable
2      (Maths, logic)
a    the relationship between two statements each of which implies the other
b    the binary truth-function that takes the value true when both component sentences are true or when both are false, corresponding to English if and only if. Symbol: <equiv> or <bicond> , as in --(p <conj> q) <equiv> --p <disj> --q,   (Also called)    biconditional

equivalence relation
n     (Logic, maths)   a relation that is reflexive, symmetric, and transitive: it imposes a partition on its domain of definition so that two elements belong to the same subset if and only if the relation holds between them
formal equivalence
n     (Logic)   the relation that holds between two open sentences when their universal closures are materially equivalent

English Collins Dictionary - English Definition & Thesaurus

## equivalence

agreement, alikeness, conformity, correspondence, equality, evenness, identity, interchangeableness, likeness, match, parallel, parity, sameness, similarity, synonymy

English Collins Dictionary - English synonyms & Thesaurus