Definition 1. Let $R$ be a binary relation. The inverse of $R$ is the relation
\[R^{-1} = \{(y, x) : (x, y) \in R\}.\]This is a set by Separation Schema:
\[R^{-1} \subseteq \im R \times \dom R.\]Inverse relation is also known as converse relation.
Proposition 1. Involutivity. For any binary relation $R$,
\[(R^{-1})^{-1} = R.\]References
- [1]
- Wikipedia contributors. Converse relation. Wikipedia, The Free Encyclopedia.