Question $4(4$ Points$)$:

Given the following relational database schema $($primary keys are bold and underlined$).$ Answer questions $4\mathrm{.}1$ to $4\mathrm{.}2$:

branch$($branch$\_$id$,$ branch$\_$name, branch$\_$city, assets$)$

customer$($customer$\_$id$,$ customer$\_$name, customer$\_$street, customer$\_$city, customer$\_$st$,$ customer$\_$zip$)$

loan$($loan$\_$number, branch$\_$id$,$ amount$)$

borrower$($customer$\_$id$,$ loan$\_$number$)$

account$($account$\_$number, branch$\_$id$,$ balance$)$

depositor$($customer$\_$id$,$ account$\_$number$)$

$4\mathrm{.}1(3$ Points$)$ For each of the following queries, write a relational algebra expression to answer the query:

a$)$ Find the branch name and branch city of all branches with assets more than $$2$ Million

b$)$ Find the branch$\_$id and loan number of all branches whose loan amount is less than $$1000.$

c$)$ Find the names, cities of residence, and state for all depositors who have accounts with balance that is less than $$5000$

$4\mathrm{.}2(1$ point$)$ For each of the following relational algebra expressions, explain the output of the expression in words:

a$)\backslash$Pi branch$\_$name $(\backslash$sigma branch$\_$city$=$Tampa$($ branch$)$

b$)\backslash$Pi loan$\_$number $(\backslash$sigma branch$\_$name$=$Orlando$($ branch loan$)$