What's the cardinality of $\displaystyle B=\{(x,X)| \ x\in A, \ X \subseteq A, \ x \in X \}$ where A is a set of n elements?

$\displaystyle |B|=|A|.|X|$ since it's the result of a binary operation.

Therefore $\displaystyle |B|=n.|X|$.

Can we say anything about $\displaystyle |X|$? At most, $\displaystyle |X|=n$, but can we say anything more definite?