Relational Algebra for Banking enterprise

Consider the following Relational database where the primary keys are underlined. Give an expression in the relational algebra to express each of the following queries:

Branch (branch-name, branch-city, address);

Customer (customer_name, street, city);

Loan (loan-number, person-name, amount);

Borrower (account-number, loan-number);

Account (account-number, branch-name, balance);

Depositor (customer-name, account-number);

i. Find all customer of bank who have an account but not a loan.

      Π_{customer_name} (depositor) - Π_{customer_name} (borrower)

ii. Find the names of all customer who lives on the same street and in the same city as Smith.   

iii. Find the names of all branches with customer who have an account in the bank who live in Dhaka. 

      Π_{branch_name} (σ_{customer_city= “Dhaka”} (customer × account × depositor))

iv. Delete all of Smith’s account records. 

     depositor ← depositor - σ_{customer_name = “Smith”} (depositor)

v. Find all customer-name, loan-number and loan-amount of the bank where borrower and loan denote two distinct relation.

      Π_{customer_name, loan_number, amount} (borrower × loan)