# equivalence relation

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Related to equivalence relation: Equivalence class

## equivalence relation

n.
A reflexive, symmetric, and transitive relationship between elements of a set, such as congruence for the set of all triangles in a plane.

## equivalence relation

n
(Logic) 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
Translations
relace ekvivalence
relacija ekvivalencije
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References in periodicals archive ?
Clearly, the Forte relation is an equivalence relation in [\[Z.sub.n]\.sup.m].
Each story portrays an equivalence relation visually and verbally without any student interaction.
The solution offered by Williamson's account is to replace the matching relation of the intiutive criterion by what he calls a "maximal M-relation", which is an equivalence relation "included" in the matching relation than which no other similarly included equivalence relation is "larger".
There are two basic elements in rough set theory, crisp set and equivalence relation ,which constitute the mathematical basis of RSs.
When a split epimorphism (f, s) : X [??] Y is algebraically exponentiable, the induced endofunctor [f.sup.*].Of on [Pt.sub.X]C is (up to a natural isomorphism) equal to the endofunctor [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [p.sub.0] and [p.sub.1] are given by the kernel equivalence relation:
Recall that an equivalence relation = defined on [A.sup.*] is a congruence if for all u, u', v, v' [member of] [A.sup.*], u [equivalent to] u' and v [equivalent to] v' imply u.v [equivalent to] u'.v'.
First, when both derived relations probes contain one node, the transitive relation comparison would have to be strongly preferred to a corresponding equivalence relation comparison, which is consistent with the outcome reported by Doran and Fields (2012).
It is merely an equivalence relation in which conceptual stimuli are class members.
Definition 2.1 [8]: Let U be a non-empty finite set of objects called the universe and R be an equivalence relation on U named as the indiscernibility relation.
A relation that is reflexive, symmetric, and transitive is called an equivalence relation. When R is an equivalence relation over A, the equivalence class of an element x [member of] A is the subset of all elements in A that bear this relation to x.
The accuracy of rough set X about the equivalence relation R is defined as

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