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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