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transitive relation

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transitive relation

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binary relation R with the property that xRy and yRz implies xRz

Key facts

Type
Binary relation
Field
Elementary algebra
Symbolic statement
∀ a , b , c ∈ X : ( a R b ∧ b R c ) ⇒ a R c {\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc}

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Article

In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.

Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c then a < c; and if x = y and y = z then x = z.

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