Antisymmetric relation

Binary relation such that if A is related to B and is different from it then B is not related to A

In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other. More formally, is antisymmetric precisely if for all or equivalently, The definition of antisymmetry says nothing about whether actually holds or not for any . An antisymmetric relation on a set may be reflexive, irreflexive, or neither reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.

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