---
title: "RA: delete loans under 1000"
subject: "Database Management System"
chapter: 3
key: "semester_6/database_management_system:ra-delete-small-loans"
source: https://www.bctengineer.com/q/semester_6/database_management_system/ra-delete-small-loans
site: BCT Engineering
---

# RA: delete loans under 1000

Database Management System · Chapter 3: Relational Languages & Relational Model

- Asked in: year not given
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/database_management_system/ra-delete-small-loans
- Whole chapter: https://www.bctengineer.com/md/semester_6/database_management_system/chapter-3

## Question

Consider the relational schema:
Acc (a_no, b_name, bal)
Branch (b_name, b_city, assets)
Customer (c_name, c_street, c_city)
Loan (l_no, b_name, amt)
Depositor (c_name, a_no)
Borrower (c_name, l_no)
Delete all loans less than $1000 in amount. (Write a relational algebra expression.)

## Short answer

Subtract loans with amt < 1000 from Loan using assignment: Loan ← Loan - σ amt < 1000 (Loan).

## Answer

Relational algebra symbols used: σ select, π project, ⋈ natural join, ∪ union, ∩ intersection, − difference, ρ rename, 𝒢 aggregate.

In relational algebra, deletion is written as an assignment: the relation is replaced by itself minus the tuples to delete.

#### Relational algebra expression
```text
Loan ← Loan − σ amt < 1000 (Loan)
```

#### Explanation
1. σ amt < 1000 (Loan) selects every loan below $1000.
2. Subtracting these tuples from Loan removes them, and the remaining loans (amt ≥ 1000) are assigned back to Loan.
3. The schema (l_no, b_name, amt) is unchanged.

If Borrower still refers to a deleted loan, those tuples should also be removed to keep referential integrity. This step must run before the Loan deletion above, because it needs the old Loan tuples to find the small loans:
```text
Borrower ← Borrower − π c_name, l_no ( Borrower ⋈ σ amt < 1000 (Loan) )
```

#### Equivalent SQL
```sql
DELETE FROM Loan WHERE amt < 1000;
```

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is deletion written in relational algebra?
   A. Loan ← Loan U σ amt<1000(Loan)
   B. π amt<1000(Loan)
   C. Loan ← σ amt<1000(Loan)
   D. As assignment: Loan ← Loan - σ amt<1000 (Loan)
   Answer: D. The relation becomes itself minus the tuples to delete. (Key point: Deletion form)

2. What does σ amt<1000(Loan) select?
   A. The loans to be kept
   B. The loans to be deleted
   C. All borrowers
   D. The schema
   Answer: B. It selects loans below $1000, which are then subtracted. (Key point: Condition)

3. Why also delete from Borrower?
   A. Borrower has the amount
   B. To change the schema
   C. Loan cannot be deleted otherwise
   D. Borrower tuples may refer to deleted loans
   Answer: D. Dangling references would break integrity. (Key point: Referential integrity)

## Close variants set in other exams

- [RA: increase loans over 10000](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-increase-loan-10) — Database Management System, chapter 3

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