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

*x*,*y*) of E where*x*≠*y*, the ordered pair (*y*,*x*) does not belong to E.In the arrow representation of an antisymmetric relation, if there is one arrow going between two elements, there is no return arrow.

More formally, a relationship ℜ is called antisymmetric when it verifies the following condition: (*x* ℜ *y* ∧ *y* ℜ *x) *⇒ *x* = *y*. In other words, if, in a relationship ℜ we have both the ordered pair (*x*, *y*) and its inverse pair (*y*, *x*), then *x* and *y* correspond to the same element.

### Examples

- The relation “…is a proper divisor of…” in the set of whole numbers is an antisymmetric relation.

If 5 is a proper divisor of 15, then 15 cannot be a proper divisor of 5. - The relation “…has a son…” in a set of people is an antisymmetric relation.

If Paul is Luke’s son, then Luke cannot be Paul’s son.