A binary relation ∼ on a set S is antisymmetric if, for all a and b in S, whenever a ∼ b and b ∼ a, then a = b. For example, the relation ≤ on the set of integers is antisymmetric, as is any partial order. Compareasymmetric relation.
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A relation R defined on a set S and having the property that
where x and y are arbitrary members of S. Examples include ‘is a subset of’ defined on sets, and ‘less than or equal to’ defined on the integers. See alsoasymmetric relation, symmetric relation.