A relation-universe of a relation of any arity is a class from which is drawn every item in every tuple of the relation. Like EXACT-DOMAIN, it is exactly those items and no other. Thus, to state that the universe of a relation is covered by some class, one can state that the relation-universe is a subclass of the covering class.
(<=> (Relation-Universe ?Relation ?Type-Class)
(And (Relation ?Relation)
(Class ?Type-Class)
(Forall (?X)
(<=> (Exists (?Tuple)
(And (Member ?Tuple ?Relation)
(Item ?X ?Tuple)))
(Instance-Of ?X ?Type-Class)))))