Symmetry (of a relation)

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A property of a binary relation. A binary relation on a set is called symmetric if for any pair of elements , implies , i.e. . An example of a symmetric relation is an equivalence.


An anti-symmetric relation on a set is a reflexive relation such that .


[a1] P.M. Cohn, "Algebra" , 1 , Wiley (1982) pp. 17ff
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Symmetry (of a relation). Encyclopedia of Mathematics. URL:
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article