If the union of two sets is the empty set, then neither of the two sets has any members. Yes, they are disjoint. If the intersection of two sets is the empty set, then they have no common elements, and they are disjoint.
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets. The union is written as A∪B or “A or B”. The intersection of two sets is a new set that contains all of the elements that are in both sets. The intersection is written as A∩B or “A and B”.