A binary relation ∼ on a set S is symmetric if, for all a and b in S, whenever a ∼ b then b ∼ a. Seeequivalence relation.
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A relation R defined on a set S and having the property that
where x and y are arbitrary elements of S. The relation ‘is equal to’ defined on the integers is symmetric. See alsoantisymmetric relation, asymmetric relation.