Find two disjoint set


Given an universum $ U$ and two sets $ A$ and $ B$ of sets of elements from $ U$ . I want to find (if such a pair exists) $ a \in A$ and $ b \in B$ : $ a \cap b \equiv \emptyset$ . Currently I can do it only in $ O(|A| \cdot |B|)$ , is there way to improve this? $ |a|, |b| \leq 32, a \in A, b \in B$ .