Starting with the following universal relation:

Books $($title$,$ isbn, author, publisherName, publisherAddress, totalCopiedOrdered, copiesInStock, publicationDate, category, sellingPrice, cost$)$And making the following assumptions about the relation:

The isbn uniquely indentifies a book.

A book may have more than author.

An author may have more than one book.

Each publisher's name is unique.

Each publisher has one unique address $($the address of their headquarters$).$

Book titles are not necessarily unique.

totalCopiesOrdered is the number of copies of a particular book that the book store has ever ordered, while copiesInStock is the number that remains unsold in their inventory.

Each book has only one publication data. A revision to a book $($Databases Illuminated, $3$rd edition, for example$)$ is given a new ISBN.

Book categories may be biography, science fiction, poetry, etc. The title alone is not sufficient to determine the category.

The selling price $($the amount the bookstore charges to a customer$)$ is always $20\%$ above

the cost $($which is the bookstore's wholesale purchase price for one copy of the book$).$

Using these assumptions $($and starting any others you need to make$),$ do parts a through d below.

a$.$ List of all non$-$trivial functional dependencies.

b$.$ Identify candidate keys and choose one primary key.

c$.$ Is the relation in $3$NF$?$ If not, find a $3$NF decomposition that is both lossless and preserves dependencies.

d$.$ Is the result from part c in BCNF$?$ If it is$,$ justify your answer. If it is not, perform another decomposition so that the result is$.$