SOLVED PROBLEMS
Problem 1. Consider the following database schema:
Opening (AccountNumber, OpenDate, OpeningBalance, TotalDeposit, TotalWithdrawal, ClosingBalance, ClosingBalanceDate, LastDepositDate, LastWithdrawalDate)
Deposit (AccountNumber, Date, Amount, Mode)
Withdrawal (AccountNumber, Date, Amount, Mode)
Account Holder (AccountNumber, Name, BuildingNumber, AreaName, StreetNumber, CityCode, PinCode, StateCode)
Cities (CityCode, CityName, StateCode)
State (StateCode, StateName)
Write the following queries in Relational algebra, tuple relational calculus and domain relational calculus.
- List of all Account Number having no deposits in Jan, 2000.
- List of all Account Number having neither any deposit nor any withdrawal in Jan, 2000.
- List of Account Number and Name of Account holders from city ROHTAK whose opening balance is not less than 9999.
- List of all cities of the state HARYANA.
- List of all Account Number who belongs to state Haryana.
- List of all city Names from which there is no Account Holders.
- List of all Account Number, which do not have any transaction after opening.
- List of all city name and their pin code for cities of state RAJASTHAN.
Solution. Relational Algebra
Tuple Relational Calculus
Domain Relational Calculus
The following naming convention is used in the queries of domain relational calculus:
- A relation is denoted by first letter of his name Relation Opening is denoted by O, Withdrawal is denoted by W.
- Each attribute of relation is denoted by first letter of its relation, “.”, and then first letter of its name Attribute “AccountNumber” in relation “Opening” is denoted by O.AN.
Problem 2. Consider the following relations:
Compute the result of the following relational algebra expression:
Problem 3. Consider the relation schemas R = (A, B, C) and S = (D, E, F). Let relations r(R) and s(S) be given. Give an expression in the tuple relational calculus that is equivalent to each of the following:
Problem 4. Let R = (A, B, C), and let r1 and r2 both be relations on schema R. Give an expression in domain relational calculus that is equivalent to each of the following:
Problem 5. Consider the relation schemas R = (A, B) and S = (A, C), and let r(R) and s(S) be relations. Write relational algebra expressions equivalent to the following domain- relational calculus expressions:
Problem 6. Consider the relation schemas R =(A, B, C) and S =(D, E, F). Let relations r(R)and s(S) be given. Give an expression in the tuple relational calculus that is equivalent to each of the following:
Problem 7. Consider the following collection of relation schemas:
professor(profname, deptname
department(deptname, building)
committee(commname, profname)
- Find all the professors who are in any one of the committees that Professor David is in.
- Find all the professors who are in at least all those committees that Professor David is in.
- Find all the professors who are in exactly (e., no more and no less) all those committees that Professor David is in.
- Find all the professors who have offices in at least all those buildings that Professor David has offices in.
Solution.
Source: Gupta Satinder Bal, Mittal Aditya (2017), Introduction to Basic Database Management System, 2nd Edition-University Science Press (2017)