 relation

—relationless, adj./ri lay"sheuhn/, n.1. an existing connection; a significant association between or among things: the relation between cause and effect.2. relations,a. the various connections between peoples, countries, etc.: foreign relations.b. the various connections in which persons are brought together: business and social relations.c. sexual intercourse.3. the mode or kind of connection between one person and another, between an individual and God, etc.4. connection between persons by blood or marriage.5. a person who is related by blood or marriage; relative: his wife's relations.6. the act of relating, narrating, or telling; narration.7. Law. a principle whereby effect is given to an act done at one time as if it had been done at a previous time.8. Math.a. a property that associates two quantities in a definite order, as equality or inequality.b. a single or multiplevalued function.9. in or with relation to, with reference to; concerning: It's best to plan with relation to anticipated changes in one's earnings.[13501400; ME relacion < L relation (s. of relatio). See RELATE, ION]Syn. 1. relationship; tie, link. 2a, 2b. association. 4. relationship, kinship. 6. recitation, recital, description.Ant. 1. independence.
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IIn logic, a relation R is defined as a set of ordered pairs, triples, quadruples, and so on.A set of ordered pairs is called a twoplace (or dyadic) relation; a set of ordered triples is a threeplace (or triadic) relation; and so on. In general, a relation is any set of ordered ntuples of objects. Important properties of relations include symmetry, transitivity, and reflexivity. Consider a twoplace (or dyadic) relation R. R can be said to be symmetrical if, whenever R holds between x and y, it also holds between y and x (symbolically, (∀x) (∀y) [Rxy ⊃ Ryx]); an example of a symmetrical relation is "x is parallel to y." R is transitive if, whenever it holds between one object and a second and also between that second object and a third, it holds between the first and the third (symbolically, (∀x) (∀y) (∀z ) [(Rxy ∧ Ryz) ⊃ Rxz]); an example is "x is greater than y." R is reflexive if it always holds between any object and itself (symbolically, (∀x) Rxx); an example is "x is at least as tall as y" since x is always also "at least as tall" as itself.II(as used in expressions)Einstein's mass energy relationLabor Management Relations Actorganizational relations* * *
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