Relation defined in a set E so that, if the ordered pairs (

*x*,*y*) and (*y*,*z*) belong to the relation, then the ordered pair (*x*,*z*) also belongs to the relation.The arrow diagram of a transitive relation in a set E includes a transit arrow (

*x*,*z*) associated with every occurrence of two arrows (*x*,*y*) and (*y*,*z*) of the diagram.### Examples

- The relation “…is the sister of…” in a family of four girls is a transitive relation.
- The relation “…is parallel to…” in a set of lines on a plane is a transitive relation.
- The relation “…is perpendicular to…” in a set of lines on a plane is a
**non-transitive relation**.