# Transitive relation

## Type of binary relation / From Wikipedia, the free encyclopedia

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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.

Type of binary relation

**Quick facts: Type, Field, Statement, Symbolic statement...**▼

Type | Binary relation |
---|---|

Field | Elementary algebra |

Statement | 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 $c$. |

Symbolic statement | $\forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc$ |

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