symmetric relation

A relation^{👁 Mathworld
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on a set is symmetric^{👁 Planetmath
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if and only if whenever for some then also .

An example of a symmetric relation on is . One relation that is not symmetric is , because but .

On a finite set^{👁 Mathworld
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with elements there are relations, of which are symmetric.

A relation that is both symmetric and antisymmetric has the property that implies . On a finite set with elements there are only such relations.