If a multivalued dependency holds and is not implied by the corresponding…

Concept: A multivalued dependency (MVD) written A →→ B holds when, for every value of A, the associated set of B-values is fixed and independent of every other attribute in the relation. A schema can carry an MVD that does not follow from its functional dependencies at all, and relational design theory recognizes exactly two structural situations in which such a non-FD-implied MVD arises when an E-R design is mapped into relations.

Application to this item:

• A many-to-many relationship set: when two entity sets are connected by a many-to-many relationship, the schema built for that relationship ties each key value on one side to a genuine SET of key values from the other side. No functional dependency forces this correspondence, so it is an independent MVD created purely by the relationship's cardinality.

• A multivalued attribute of an entity set: when a single entity type carries an attribute that can legitimately take several values at once for one entity, the schema built for that attribute again ties one key value to a whole set of attribute values, independent of every other attribute. This is a second, independent, non-FD-implied MVD, and it needs no relationship set at all.

Cross-check: a one-to-many relationship set does not need this reasoning at all. When one entity relates to many entities, each entity on the 'many' side is associated with exactly one entity on the 'one' side, and mapping this into relations places the 'one' side's key as a foreign key inside the 'many' side's schema. That correspondence is already an ordinary functional dependency — the key of the 'many'-side entity determines a single value of the 'one'-side key, not a set of values — so no independent multivalued dependency needs to be invoked there. That rules out a one-to-many relationship set as a source of a non-FD-implied MVD.

Result: since both structural situations independently produce a genuine multivalued dependency, the complete answer names both together — a many-to-many relationship set and a multivalued attribute of an entity set.