Consider the following tables, Loan and Borrower, of a bank. Loan: loan_number | branch_name | amount L11 | Begum Hills | 20000 L14 | Kondapur | 50000 L15 | SR Nagar | 40000 L22 | SR Nagar | 20000 L25 | Balanagar | 80000 L25 | Kondapur | 70000 L19 | SR Nagar | 62000 Borrower: customer_name | loan_num Anand | L11 Gopak | L11 Karteek | L14 Ankita | L15 Gopak | L19 Karteek | L22 Smit | L23 Karteek | L25 Query: pi_{branch_name, customer_name} ( Loan |><| Borrower ) where |><| denotes natural join. The number of tuples returned by the above relational algebra query is ____________ (Answer in integer)

GATE 2025 · Databases · Relational Algebra · medium

Answer: The number of tuples returned by the query is 7.

1. Perform the natural join: match loan_number = loan_num: Go through each Borrower tuple and find matching Loan tuples: - Anand, L11 -> Loan(L11, Begum Hills, 20000) => (L11, Begum Hills, 20000, Anand) - Gopak, L11 -> Loan(L11, Begum Hills, 20000) => (L11, Begum Hills, 20000, Gopak) - Karteek, L14 -> Loan(L14, Kondapur, 50000) => (L14, Kondapur, 50000, Karteek) - Ankita, L15 -> Loan(L15, SR Nagar, 40000) => (L15, SR Nagar, 40000, Ankita) - Gopak, L19 -> Loan(L19, SR Nagar, 62000) => (L19, SR Nagar, 62000, Gopak) - Karteek, L22 -> Loan(L22, SR Nagar, 20000) => (L22, SR Nagar, 20000, Karteek) - Smit, L23 -> NO matching Loan row => DROPPED - Karteek, L25 -> Loan(L25, Balanagar, 80000) => (L25, Balanagar, 80000, Karteek) - Karteek, L25 -> Loan(L25, Kondapur, 70000) => (L25, Kondapur, 70000, Karteek) Total join result: 8 tuples.
2. Apply projection and count distinct tuples: After projection, the 8 tuples become: 1. (Begum Hills, Anand) 2. (Begum Hills, Gopak) 3. (Kondapur, Karteek) 4. (SR Nagar, Ankita) 5. (SR Nagar, Gopak) 6. (SR Nagar, Karteek) 7. (Balanagar, Karteek) 8. (Kondapur, Karteek) <-- same as tuple 3! Check for duplicates: (Kondapur, Karteek) appears from both L14 and L25-Kondapur. So after deduplication: 7 distinct tuples.