Each publisher name is unique. Each publisher has a unique address, the address of the firm's headquarters. Titles are not unique. Each book has only one publication date. The category might be biography, science fiction, poetry, and so on.
Categories are unique.
The title alone is not sufficient to determine the category. These relations should form an irreducible set. Prove that the identified key is actually a primary key. Find a 3NF lossless join decomposition that preserves dependencies. Justify your answer.