Transitive Relation
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.