Problem $1$: Consider the LIBRARY relational 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 algebra expressions for the following queries on the

LIBRARY database:

BOOK$\_$LOANS

Figure $6\mathrm{.}14$

A relational database

schema for a LIBRARY

database.

$($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$)$ For each library branch, retrieve the branch name and the total number of

books loaned out from that branch.