# Transitive relation

In mathematics, a 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*. Each partial order as well as each equivalence relation needs to be transitive.

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Type | Binary relation |
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Field | Elementary algebra |

Statement | A relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . |

Symbolic statement |