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.
- 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.