Your example is not union-closed. "A collection, or family, of sets is considered “union-closed” if the union of any two sets in the family equals any existing

Your example is not union-closed. "A collection, or family, of sets is considered “union-closed” if the union of any two sets in the family equals any existing set in the family." EDIT: In your hypothetical collection of sets, the union of "2" and "3" would produce the set "2,3" which is not an enumerated set in your list.