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In Entity Relationship Model, can the supporting (or identifying) relationships of the weak entities be many-many or one-one rather than many-one?

Suppose I have a customer entity (C), a video entity (V) and a weak entity reservation (R). C - R has a one-many relationship and it's a supporting relationship for R. However between V - R the same one-many relationship wouldn't make sense, since a video shouldn't appear in two different reservations.

So I wonder if a one-one relationship can be a supporting one for the weak entity? Or should it be a normal one-one instead of a supporting one?

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If you are running a video rental store, then whether or not your children eat depends very much on a video appearing in as many reservations as possible.

In your example, RESERVATION is a weak entity which relies on both the FK to CUSTOMER and the FK to VIDEO in addition to a further attribute, perhaps date, to comprise its primary key.

It is not possible for a M:N relationship to be supporting for a weak entity (although the intersection table which resolves a M:N relationship can be a weak entity). This is because a supporting relationship needs to be to a particular entity object. A set of entity objects can't identify something in relational algebra.

It is possible for a 1:1 relationship to be supporting for a weak entity, although this would be rare "in the wild". I could imagine it coming up in the context of situations that would typically be 1:M, but where there is a business rule that restricts the child to one at a time.

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