Relation in a set E so that for the ordered pairs (

*x*,*y*) and (*y*,*z*) to belong to the graph, the ordered pair (*x*,*z*) must not.In the arrow representation of an antitransitive relation, every time that we have the ordered pairs (

*x*,*y*) and (*y*,*z*), we do not have the ordered pair (*x*,*z*).In this representation, for example, we have: (*a*, *b*) and (*b*, *c*), but not (*a*, *c*).

### Examples

- The relation “…is perpendicular to…” in a set of lines of the plane is an antitransitive relation.

If d ⊥ d\(_{1}\) and d\(_{1}\)⊥ d\(_{2}\), it is impossible that d ⊥ d\(_{2}\), because d ⁄ ⁄ d\(_{2}\). - The relation “…is the mother of…” in a set of people is an antitransitive relation.

If Anne is Julie’s mother and Julie is Marie’s mother, then Anne is Marie’s grandmother and cannot be Marie’s mother.