Composition of relations

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, and its result is called a relative product.^: 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" ( $yPz$ ).

U=BP\quad {\text{ is equivalent to: }}\quad xByPz{\text{ if and only if }}xUz.

Beginning with Augustus De Morgan, the traditional form of reasoning by syllogism has been subsumed by relational logical expressions and their composition.

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