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Mathematics-Online lexicon:

Relation

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If elements of a set $ A$ are related to elements of a set $ B$, this can be expressed via a (binary) relation. Such a relation consists of ordered pairs $ (a,b)$ of related elements.

A relation $ R$ is therefore a subset of the cartesian product of $ A$ and $ B$. The notation $ a\operatorname{R}b$ is used to state that $ a$ is related to $ b$:

$\displaystyle a \operatorname{R}b \Leftrightarrow (a,b) \in R \subseteq A \times B\,. $

(Authors: Hörner/Abele)

see also:

[Examples]
  automatically generated 9/18/2007