What is the best way to express the set of sets that has no element in common with another set? I am trying to express the following: I have a set $A$ and the powerset (set of all subsets of $A$) $P(A)$. I have another set $S \in P(A)$, and I want to get the sets in $P(A)$ with no element in common with $S$.
The way I express this is $$X \in P(A): X \cap S = \{\}$$
Is there a more concise way or a special notation from set theory?

You could use union of disjoint subsets to achieve the same thing: $X, Y \in P(A), X \sqcup Y \equiv A$
