Definition#

A relation \(\rho\) on the set \(S\) is symmetric if \(a\rho b\) implies \(b \rho a\).

Example#

Define \(\rho\) via \(a \rho b\) if and only if \(\left| a-b \right| \leq 10\). Then \(\rho\) is symmetric.

Source#

Gregory T. Lee. Abstract Algebra. 1st ed. Springer Cham, 2018. pp. 6.