Consider the following relational schemas for a library database : Book (Title, Author, Catalog_no, Publisher, Year, Price) Collection(Title, Author, Catalog_no) with the following functional dependencies : I. Title, Author → Catalog_no II. Catalog_no → Title, Author, Publisher, Year III. Publisher, Title, Year → Price Assume (Author, Title) is the key for both schemas. Which one of the following is true ?
Book is in 2NF and Collection in 3NF.
Collection(Title, Author, Catalog_no): the dependencies Title, Author → Catalog_no and Catalog_no → Title, Author have keys on the left, so Collection is in 3NF (indeed BCNF).
Book: candidate keys are (Title, Author) and Catalog_no; no non-prime attribute depends on a proper part of a key, so Book is in 2NF.
But Publisher, Title, Year → Price has a non-key left side and a non-prime right side, a transitive dependency, so Book is not in 3NF.
Hence Book stops at 2NF while Collection reaches 3NF.
Hence, Book is in 2NF and Collection in 3NF.
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