Re: Many-to-Many Must Have at Least One Descriptive Attribute
Posted by: Bill Karwin
Date: December 01, 2006 08:15PM

As far as I understand the theory, the functional dependencies are what you stated in your original post.

The functional dependency between X -> Y and the multivalued dependency between X ->> Y are both considered trivial if Y is a subset of X, as in this case when Y is part of the compound key formed by X.

book_id, lang_id -> lang_id 
book_id, lang_id -> book_id

The above states that if we know book_id and lang_id, then we know lang_id. And likewise we know book_id.

book_id ->> lang_id
lang_id ->> book_id

The above states that for each book, there may be multiple languages, and we can infer the set of languages for a given book. Likewise, for each language, there may be multiple books, and we can infer the set of books for a given language.

This is trivially true when the relation consists only of book_id and lang_id. It's said that if X union Y is the full set of attributes in the relation, then of course X ->> Y is true. Things would get more complicated if there were any other attribute columns to take into account.

Here's a good web page with lecture notes on MVD:
http://www.cs.jcu.edu.au/Subjects/cp1500/1998/Lecture_Notes/normalisation/mvd.html

Regards,
Bill K.

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