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, ( 2200; x) ( 2200; y) [Rxy 2283; 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, ( 2200; x) ( 2200; y) ( 2200; z ) [(Rxy 2227; Ryz) 2283; Rxz]); an example is "x is greater than y." R is reflexive if it always holds between any object and itself (symbolically, ( 2200; x) Rxx); an example is "x is at least as tall as y" since x is always also "at least as tall" as itself.