# Composition of relations

## Mathematical operation / From Wikipedia, the free encyclopedia

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In the mathematics of binary relations, the **composition of relations** is the forming of a new binary relation *R*; *S* from two given binary relations *R* and *S*. In the calculus of relations, the composition of relations is called **relative multiplication**,^{[1]} and its result is called a **relative product**.^{[2]}^{: 40 } Function composition is the special case of composition of relations where all relations involved are functions.

The word uncle indicates a compound relation: for a person to be an uncle, he must be the brother of a parent. In algebraic logic it is said that the relation of Uncle ($xUz$) is the composition of relations "is a brother of" ($xBy$) and "is a parent of" ($yPz$).

Beginning with Augustus De Morgan,^{[3]} the traditional form of reasoning by syllogism has been subsumed by relational logical expressions and their composition.^{[4]}