Final answer:
The correct SQL command to display book information for the BUSINESS category is option c), which uses a JOIN clause and a WHERE filter on the 'BOOKS' category.
Step-by-step explanation:
The correct way to display the title, publication date, and publisher name of each book in the BUSINESS category is by using a SQL JOIN clause to combine rows from the BOOKS table and the PUBLISHER table, where the books are filtered by the BUSINESS category. The appropriate query which fulfills this requirement is:
c) SELECT title, publication_date, publisher_name
FROM books
JOIN publisher ON books.publisher_id = publisher.publisher_id
WHERE books.category = 'BUSINESS';
This SQL command first joins the two tables on their related publisher_id, ensuring that each book's information is associated with the correct publisher. Then the WHERE clause filters the results to only include books that fall into the 'BUSINESS' category.