Consider the LIBRARY relational database schema shown below which is used to keep track of books, borrowers, and book loans. Referential integrity constraints are shown as directed arcs. Write down relational expressions for the following queries:

1. How many copies of the book titled The Lost Tribe are owned by the library branch whose name is Sharpstown?

2. How many copies of the book titled The Lost Tribe are owned by each library branch?

3. Retrieve the names of all borrowers who do not have any books checked out.

4. For each book that is loaned out from the Sharpstown branch and whose Due_date is today, retrieve the book title, the borrowers name, and the borrowers address.

5. For each library branch, retrieve the branch name and the total number of books loaned out from that branch