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Related to equivalence relation: Equivalence class
See: parity
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On the other hand, if the converse is true, then parallelism is an equivalence relation on the residues.
We also defined symmetric, transitive, reflexive and equivalence relations on the NP-soft sets.
Definition 3 Let P be a poset and let ~ be an equivalence relation on P.
The universal equivalence relation E = T x T is arranged while the identity relation E = {(x,x) : x [member of] t} is not whenever t contains more than one element.
The first published study designed to investigate the relationship between language and stimulus equivalence or derived equivalence relations was reported in the mid-eighties (Devany, et al.
Students from both Groups 1 and 2 were asked to write their reactions to the lesson on relations, their properties, and equivalence relations.
Therefore, any equivalence relation on pitch or pitch-class sets other than transposition is necessarily ad hoc, at least in the context of the interval system.
Let U be a non-null set and R be an equivalence relation on U.
In stark contrast with the above result, recall that a regular category is Mal'tsev if and only if every reflexive relation in it is an equivalence relation, while on the other hand, the so-called Lawvere condition "all internal reflexive graphs are internal groupoids" means that the category is naturally Mal'tsev [4,12].
An equivalence relation [equivalent to] defined on [A.
If we examine the extensions of these scaled similarity relations with regard to maximal similarity, what becomes strikingly apparent is the fact that maximal similarity--the extreme of the degree/extreme predicate IS-SIMILAR--TO--corresponds in extension precisely to some equivalence relation with a distinguished position in pc set-class theory.
They are also essentially surjective, since, in an efficiently regular category, any equivalence fibration which is discretely cofibered above an effective equivalence relation is itself effective.