Relation defined in a set E so that, for every ordered pair of elements (

*x*,*y*) of \(E\times E\), if*x*is in relation with*y*, then*y*is in relation with*x*.- The arrow diagram of a symmetric relation in a set E includes a return arrow every time that there is an arrow going between two elements.
- A relation defined in a set E so that, for every ordered pair (
*x*,*y*) of E \(\times\) E, with*x*≠*y*, (*y*,*x*) is not an ordered pair of the relation, is called an**antisymmetric relation**. - A relation defined in a set E that is neither symmetric nor antisymmetric is a
**non-symmetric relation**. - A relation defined in a set E so that, for all pairs of elements {
*x*,*y*}, either one of the ordered pairs (*x*,*y*) or (*y*,*x*) belong to the relation, but never both at the same time, is an**asymmetric relation**.

### Examples

- In a set of lines of a plane, the relation “…is perpendicular to…” is a symmetric relation.
- In a set of numbers, the relation “…divides…” is an antisymmetric relation.
- In a set of numbers, the relation “…is less than…” is an asymmetric relation.