Complex sentence: However, the converse is not true: the intersection of the collection is empty, but the collection is "not" pairwise disjoint-in fact, there are no two disjoint sets in the collection.
Split into simpler sentences: However, the converse is not true: the intersection of the collection is empty, but the collection is "not" pairwise disjoint. In fact, there are no two disjoint sets in the collection.