# Transitive Relation

## Transitive Relation

Relation defined in a set E so that, if the ordered pairs (xy) and (yz) belong to the relation, then the ordered pair (xz) also belongs to the relation.

The arrow diagram of a transitive relation in a set E includes a transit arrow (xz) associated with every occurrence of two arrows (xy) and (yz) 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.