Symmetry (of a relation)

From Encyclopedia of Mathematics
Jump to: navigation, search

A property of a binary relation. A binary relation $R$ on a set $A$ is called symmetric if for any pair of elements $a,b \in A$, $aRb$ implies $b R a$, i.e. $R \subseteq R^{-1}$. An example of a symmetric relation is an Equivalence relation.


An anti-symmetric relation on a set $A$ is a reflexive relation $R$ such that $R \cap R^{-1} \subseteq \Delta = \{ (x,x) : \forall x \in A \}$.


[a1] P.M. Cohn, "Algebra" , 1 , Wiley (1982) pp. 17ff
How to Cite This Entry:
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