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relation

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.

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1.	(mathematics)	relation - A subset of the product of two sets, R : A x B. If (a, b) is an element of R then we write a R b, meaning a is related to b by R. A relation may be: reflexive (a R a), symmetric (a R b => b R a), transitive (a R b & b R c => a R c), antisymmetric (a R b & b R a => a = b) or total (a R b or b R a). See equivalence relation, partial ordering, pre-order, total ordering.
2.	(database)	relation - A table in a relational database.