Converse Relation

🅟 Feb 21, 2026

  🅤 Feb 24, 2026

Set Theory > Relations

DEF-RCV. Converse Relation.

Let $R$ be a binary relation. The converse relation of $R$ is

\[R^{-1} = \{(y,x)\in\operatorname{ran}R\times\operatorname{dom}R:x\,R\,y\}.\]

PROP-RCV-DB.

For any binary relation $R$,

\[(R^{-1})^{-1} = R.\]

PROP-RCV-SYM.

A binary relation $R$ is symmetric if and only if $R=R^{-1}$.