(5 points each) Write the following queries in relational algebra, using the schema provided above. • If a query is long, feel free to break it up into a series of queries with intermediate answers stored in temporary relations (e. g. "let temp ="). • You can use abbreviations for Relational Algebra symbols such as S for SELECTION, P for PROJECTION, * for NATURAL JOIN, - for SET DIFFERENCE • Your queries must not be "state-dependent", that is, they should work without modification even if another instance of the database is given. (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? (c) Retrieve the names of all borrowers who do not have any books checked out. (d) For each book that is loaned out from the Sharpstown branch and whose DueDate is prior to "September 1, 2018", retrieve the book title, the borrower’s name, and the borrower’s address. (e) For each book authored (or coauthored) by Stephen King, retrieve the title and the number of copies owned by the library branch whose name is "Central". (f) Retrieve all book titles