Editing Antisymmetric relation (section)

== Properties ==

[[File:Symmetric-and-or-antisymmetric.svg|thumb|Symmetric and antisymmetric relations|340x340px]]

[[Partial order|Partial]] and [[total order]]s are antisymmetric by definition. A relation can be both [[Symmetric relation|symmetric]] and antisymmetric (in this case, it must be [[Coreflexive relation|coreflexive]]), and there are relations which are neither symmetric nor antisymmetric (for example, the "preys on" relation on biological [[species]]).

Antisymmetry is different from [[Asymmetric relation|asymmetry]]: a relation is asymmetric if and only if it is antisymmetric and [[Irreflexive relation|irreflexive]].