Let $U$ be a finite universal set, and let $A, B \subseteq U$ be disjoint subsets. We wish to find the number of subsets $X \subseteq U$ that satisfy the relation $A \cap X = B \setminus X$. If $|U| = n$, $|A| = a$, and $|B| = b$, how many such subsets $X$ exist?