inverse (relation)

The inverse of a binary relation $R\subseteq A\times B$ is the relation $R^{-1}\subseteq B\times A$, where $R^{-1}=\{⟨y,x⟩:⟨x,y⟩\in R\}$. Put simply, the inverse is the original relation but for each ordered pair, the first components are swapped with the second.