Transitive relation

Transitive relation
TypeBinary relation
FieldElementary algebra
StatementA relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to .
Symbolic statement

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.


Transitive relation

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