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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, and its result is called a relative product. 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, the traditional form of reasoning by syllogism has been subsumed by relational logical expressions and their composition. (en) In de abstracte verzamelingenleer kan met behulp van twee relaties tussen verzamelingen soms een nieuwe relatie gevormd worden, de samengestelde relatie. Als namelijk in een zekere relatie staat tot , en staat op zijn beurt weer in een relatie met , dan is er dus een relatie tussen en , die de samengestelde relatie heet. (nl) 数学における二項関係の合成（ごうせい、英: composition）は、与えられた二つの関係 R, S から新たな関係 S ∘ R を作り出す操作である。この最もよく知られた特別の場合が写像の合成である。 (ja) Złożenie relacji dwuargumentowych – szczególna konstrukcja relacji dwuargumentowych z dwóch innych relacji dwuargumentowych, a zarazem wynik tej konstrukcji. Przypadkiem szczególnym złożenia relacji jest złożenie funkcji. (pl) |
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In de abstracte verzamelingenleer kan met behulp van twee relaties tussen verzamelingen soms een nieuwe relatie gevormd worden, de samengestelde relatie. Als namelijk in een zekere relatie staat tot , en staat op zijn beurt weer in een relatie met , dan is er dus een relatie tussen en , die de samengestelde relatie heet. (nl) 数学における二項関係の合成（ごうせい、英: composition）は、与えられた二つの関係 R, S から新たな関係 S ∘ R を作り出す操作である。この最もよく知られた特別の場合が写像の合成である。 (ja) Złożenie relacji dwuargumentowych – szczególna konstrukcja relacji dwuargumentowych z dwóch innych relacji dwuargumentowych, a zarazem wynik tej konstrukcji. Przypadkiem szczególnym złożenia relacji jest złożenie funkcji. (pl) 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. Function composition is the special case of composition of relations where all relations involved are functions. Beginning with Augustus De Morgan, the traditional form of reasoning by syllogism has been subsumed by relational logical expressions and their composition. (en) |
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Composition of relations (en) 関係の合成 (ja) Samengestelde relatie (nl) Złożenie relacji (pl) |
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