Given the following relational database schema (primary keys are bold and underlined). Answer questions 4.1 to 4.2:

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)

4.1 (3 Points) For each of the following queries, write a relational algebra expression to answer the query:

a) Find the names of all customers who live in Plymouth and have the name Bronson.

b) Find the names and zip codes of all customers who have loans.

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

4.2 (2 point) For each of the following relational algebra expressions, explain the output of the expression in words:

_{branch_name} (_{branch_city=Tampa}( branch)

_{loan_number} (_{branch_name=Orlando}( branch loan)