We have the problem, Let $A$ be a non-empty set and let B be a subset of the powerset of A. Define a relation $R$ from A to B by $xRY $ if $x \in Y$
I've defined it as follows; $$R={\{(x, Y)\subseteq A\times B |x \in A \wedge x\in Y}\}$$
or should I also state Y is a subset of B?