View source for Symmetry (of a relation)

A property of a [[Binary relation|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]].



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

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  P.M. Cohn,   "Algebra" , '''1''' , Wiley  (1982)  pp. 17ff</TD></TR></table>