Consider the LIBRARY relational database schema shown in Figure, which is used to keep track of books, borrowers, and book loans. Referential integrity constraints are shown as directed arcs in Figure. Write down relational expressions for the following queries: a. How many copies of the book titled The Lost Tribe are owned by the library branch whose name is Sharpstown? b. How many copies of the book titled The Lost Tribe are owned by each library branch? (, you should output the library branch name along with the number-of-copies information)

c. Retrieve the name of all library branches that have every book authored (or coauthored) by Jim Butcher.

BOOK Book id Title Publisher_ name BOOK AUTHORS Book _id Author_name PUBLISHER Name Address Phone BOOK COPIES Book id Branch idNo of copies BOOK LOANS Book id Branch id Card no Date out| Due_date LIBRARY BRANCH Branch_id Branch name Address BORROWER Card no Name Address Phone