relation

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 multiple-valued 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.
[1350-1400; 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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I
In 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 two-place (or dyadic) relation; a set of ordered triples is a three-place (or triadic) relation; and so on. In general, a relation is any set of ordered n-tuples of objects. Important properties of relations include symmetry, transitivity, and reflexivity. Consider a two-place (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 relation
Labor Management Relations Act
organizational relations

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Universalium. 2010.

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