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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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relation

1. Law the principle by which an act done at one time is regarded in law as having been done antecedently

2. Law the statement of grounds of complaint made by a relator

3. Logic Maths

a. an association between ordered pairs of objects, numbers, etc., such as … is greater than …

b. the set of ordered pairs whose members have such an association

4. Philosophy

a. internal relation a relation that necessarily holds between its relata, as 4 is greater than 2

b. external relation a relation that does not so hold

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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.