The relation on powersets associated to $R$ is the relation
\[ \mathcal{P}\webleft (R\webright )\colon \mathcal{P}\webleft (A\webright )\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}\mathcal{P}\webleft (B\webright ) \]
defined by1
\[ \mathcal{P}\webleft (R\webright )^{V}_{U}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\mathbf{Rel}\webleft (\chi _{\text{pt}},V\mathbin {\diamond }R\mathbin {\diamond }U\webright ) \]
for each $U\in \mathcal{P}\webleft (A\webright )$ and each $V\in \mathcal{P}\webleft (B\webright )$.
1Illustration:
