"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." Your family is

"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." Your family isn't union closed because it doesn't include {1, 2}, the union of {1} and {2}.