# GATE | GATE CS 2008 | Question 69

• Last Updated : 24 Sep, 2021

Consider the following relational schemes for a library database:
Book (Title, Author, Catalog_no, Publisher, Year, Price)
Collection (Title, Author, Catalog_no)

with in 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 schemes. Which of the following statements is true?
(A) Both Book and Collection are in BCNF
(B) Both Book and Collection are in 3NF only
(C) Book is in 2NF and Collection is in 3NF
(D) Both Book and Collection are in 2NF only

Explanation:

```Book (Title, Author, Catalog_no, Publisher, Year, Price)
Collection (Title, Author, Catalog_no) ```

with in 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 schemes ```
• The table “Collection” is in BCNF as there is only one functional dependency “Title Author –> Catalog_no” and {Author, Title} is key for collection.
• Book is not in BCNF because Catalog_no is not a key and there is a functional dependency “Catalog_no –> Title Author Publisher Year”.
• Book is not in 3NF because non-prime attributes (Publisher Year) are transitively dependent on key [Title, Author].
• Book is in 2NF because every non-prime attribute of the table is either dependent on the whole of a candidate key [Title, Author], or on another non prime attribute.
In table book, candidate keys are {Title, Author} and {Catalog_no}. In table Book, non-prime attributes (attributes that do not occur in any candidate key) are Publisher, Year and Place

Please refer Database Normalization | Normal Forms for details of normal forms.

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