A binary relation *R* over a set *X* is **antisymmetric** if it holds for all *a* and *b* in *X* that if *aRb* and *bRa* then *a* = *b*. Many interesting binary relations such as partial orders and total orders have this property.

Note that antisymmetry is not the opposite of *symmetry?* (*aRb* implies *bRa*), that is, it does not necessarily hold for an antisymmetric relation that *aRb* implies that not *bRa*. In fact, a binary relation can be antisymmetric and symmetric? at the same time if, and only if, no two different elements are related.