# The primary key of a relationship set in an E-R data model

1. Mar 12, 2008

### Eus

Hi Ho!

I have posted this same question about three weeks ago on MySQL forum (http://forums.mysql.com/read.php?125,197805,197805) and on the mailing list of the book itself about two weeks ago (db-book-list@cs.yale.edu). But, still there is no response at all. Therefore, I try my luck by posting the question here.

On a book, which is published by McGraw Hill, titled Database System Concepts, 4th Edition, by Silberschatz, Korth, and Sudarshan, I found a contradiction that I would like to clarify with you.

The problem is within chapter 2, which starts on page 27 and ends on page 77, that discusses Entity-Relationship Model.
On page 36 in a section that discusses the key to distinguish among the various relationships of a relationship set, there is the following statement:

In my opinion, the last sentence is wrong. The right one should be as follows:

"The composition of the primary key for a relationship set does not depend on the set of attributes associated with the relationship set $R$."

The following evidences support my argument:
1. On page 32 in a section that discusses Relationship Sets there is the following statement:

"A relationship instance in a given relationship set must be uniquely identifiable from its participating entities, without using the descriptive attributes."

Previously, the descriptive attributes are defined as attributes that are associated with a relationship set.
With other words, the composition of the primary key for a relationship set does not depend on the set of attributes associated with the relationship set R.

2. On page 36 just below the concerned statement, it is written that:

Because in both of the above cases the superkey (i.e., a set of one or more attributes that, taken collectively, allow us to identify uniquely a relation in a relationship set) is just
$$primary-key(E_{1})\ \bigcup\ primary-key(E_{2})\ \bigcup\ ...\ \bigcup\ primary-key(E_{n})$$,
the composition of the primary key for a relationship set does not depend on ${a_{1},\ a_{2},\ ...,\ a_{m}}$ (i.e., the set of attributes associated with the relationship set $R$).
With other words, in both of the above cases, the set of attributes
$$primary-key(E_{1})\ \bigcup\ primary-key(E_{2})\ \bigcup\ ...\ \bigcup\ primary-key(E_{n})$$
is sufficient to describes an individual relationship in set $R$.
Therefore, the composition of the primary key for a relationship set does not depend on the set of attributes associated with the relationship set $R$.

To conclude, is it true that the composition of the primary key for a relationship set does not depend on the set of attributes associated with the relationship set $R$?

In practice there are some examples that require the use of descriptive attributes to form the primary key of a relationship set. One such examples is as follows:

Consider two entity sets: Student and Course along with one relationship set: Took that describes a many-to-many relationship between Student and Course, as well as one descriptive attribute associated with the relationship set: Quarter.

If one student is only permitted to take a course once, then the primary key of the relationship set will be
$$primary-key(Student)\ \bigcup\ primary-key(Course)$$

But, if one student is permitted to take a course more than once, then the primary key of the relationship set will be
$$primary-key(Student)\ \bigcup\ primary-key(Course)\ \bigcup\ {Quarter}$$

If it is true that:
"The composition of the primary key for a relationship set does not depend on the set of attributes associated with the relationship set $R$.",
the relationship set of the aforementioned example must be transformed to an entity set named: Academic Quarter in spite of the fact that we are still working on the E-R data model (usually we start creating bridging-tables and other necessary transformations when we translate the E-R data model into the relational data model).

Is such transformation a common practice when modeling data with E-R data model because the composition of the primary key for a relationship set does not depend on the set of attributes associated with the relationship set $R$?

Thank you very much.

Best regards,
Eus