GATE DA 2025 Set 1 — Question 62
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Database Management & Warehousing → Relational Algebra → Join & Division
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Question
Consider the following tables, Loan and Borrower, of a bank.Loan
Borrower
Query:
where denotes natural join.The number of tuples returned by the above relational algebra query is __________
(Answer in integer)
| loan_num | branch_name | amount |
|---|---|---|
| L11 | Banjara Hills | 90000 |
| L14 | Kondapur | 50000 |
| L15 | SR Nagar | 40000 |
| L22 | SR Nagar | 25000 |
| L23 | Balanagar | 80000 |
| L25 | Kondapur | 70000 |
| L19 | SR Nagar | 65000 |
| customer_name | loan_num |
|---|---|
| Anand | L11 |
| Karteek | L11 |
| Karteek | L14 |
| Ankita | L15 |
| Gopal | L19 |
| Karteek | L22 |
| Karteek | L23 |
| Sunil | L23 |
| Sunil | L25 |
where denotes natural join.The number of tuples returned by the above relational algebra query is __________
(Answer in integer)
Correct answer
1 to 1
Solution
The query uses the division operator . The expression returns tuples from the projection of that are associated with every tuple in .
We need to find the
1.Divisor ():
The set of all branch names in the Loan table:2.Dividend ():
We join Loan and Borrower to associate customers with branches via their loans:- Anand: L11 Banjara Hills
- Karteek: L11 Banjara Hills, L14 Kondapur, L22 SR Nagar, L23 Balanagar
- Ankita: L15 SR Nagar
- Gopal: L19 SR Nagar
- Sunil: L23 Balanagar, L25 Kondapur
We need to find the
customer_name that is associated with ALL branches in set .- Karteek is associated with: Banjara Hills, Kondapur, SR Nagar, Balanagar. (Matches all 4)
- Sunil is associated with: Balanagar, Kondapur. (Missing Banjara Hills, SR Nagar)
- Anand is associated with: Banjara Hills. (Missing others)
- Ankita is associated with: SR Nagar. (Missing others)
- Gopal is associated with: SR Nagar. (Missing others)
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