Here are some examples of inverses of relations.
- Less Than Equal Signs. We have $\webleft (\mathord {\leq }\webright )^{\dagger }=\mathord {\geq }$.
- Greater Than Equal Signs. Dually to Item 1, we have $\webleft (\mathord {\geq }\webright )^{\dagger }=\mathord {\leq }$.
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Functions. Let $f\colon A\to B$ be a function. We have
\begin{align*} \text{Gr}\webleft (f\webright )^{\dagger } & = f^{-1},\\ \webleft (f^{-1}\webright )^{\dagger } & = \text{Gr}\webleft (f\webright ). \end{align*}
