Please note: You may need to learn how to type symbols such as $,,$ etc.. with some subscriptions. This assignment focusing on how to use relational algebra to write expressions for answering queries

$-$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:

$($a$)$ How many copres or tne vook nued nue cost rribe" 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?

$\backslash$table$[[$TABLE T$1,$TABLE T$2],[P,$a$,R,$A$,$B$,$C$],[10,$a$,5,10,$b$,6],[15,$b$,8,25,$c$,3],[25,$a$,6,10,$b$,5]]$

a

b

c

d

e$.T1T2$

f$.$ AND $T1.R=T2.C$

$($c$)$ For each library branch, retrieve the branch name and the total number of books loaned out from that branch.