---
title: "RA: employees on no project"
subject: "Database Management System"
chapter: 3
key: "semester_6/database_management_system:ra-emp-no-project"
source: https://www.bctengineer.com/q/semester_6/database_management_system/ra-emp-no-project
site: BCT Engineering
---

# RA: employees on no project

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

- Asked in: year not given
- Video: [Relational Algebra Expressions with Employee, Department & Project Tables | DBMS Module 2 BCS403 VTU](https://www.youtube.com/watch?v=99trDPSh7XY) — Express VTU 4 All
- 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-emp-no-project
- Whole chapter: https://www.bctengineer.com/md/semester_6/database_management_system/chapter-3

## Question

Consider the relational schema:
employee (e_no, name, address)
project (p_no, p_name)
work (e_no, p_no)
part (part_no, part_name, qty, size)
use (e_no, p_no, part_no, number)
Print names of employees not working on any project. (Write a relational algebra expression.)

## Short answer

All employee numbers minus those in work, join with employee and project name: π name (employee ⋈ (π e_no(employee) − π e_no(work))).

## Answer

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

#### Relational algebra expression
```text
π name ( employee ⋈ ( π e_no (employee) − π e_no (work) ) )
```

#### Explanation
1. π e_no (employee) is the set of all employee numbers.
2. π e_no (work) is the set of employees who work on at least one project.
3. The difference gives the e_no of employees who appear in no work tuple.
4. Joining back with employee gets their details, and π name prints the names.

The difference operator is needed because "not" cannot be expressed by selection alone.

#### Equivalent SQL
```sql
SELECT name FROM employee
WHERE e_no NOT IN (SELECT e_no FROM work);
```

## Check yourself

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

1. Why is the difference operator used?
   A. Difference joins two relations
   B. Selection can express 'not' directly
   C. Difference removes duplicates
   D. 'Not' cannot be expressed by selection alone; subtract working employees from all employees
   Answer: D. Employees not on any project = all e_no minus e_no in work. (Key point: Difference operator)

2. Which expression gives the e_no of employees on no project?
   A. pi e_no(work) - pi e_no(employee)
   B. pi e_no(employee) - pi e_no(work)
   C. pi e_no(employee) U pi e_no(work)
   D. pi e_no(employee) ∩ pi e_no(work)
   Answer: B. Subtract the working set from the full set. (Key point: Expression core)

3. Why join the difference with employee?
   A. To remove duplicates
   B. To make operands union-compatible
   C. To count employees
   D. To get the details such as name for those e_no values
   Answer: D. The difference yields only e_no; name is in employee. (Key point: Joining back)

## Close variants set in other exams

- [RA: employees on project DBMS](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-emp-project-dbms) — Database Management System, chapter 3

## Related in Database Management System

- [RA: employee-projects with no part used](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-emp-project-no-part) — Database Management System, chapter 3
- [RA: employees in both DBMS and MIS](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-emp-both-dbms-mis) — Database Management System, chapter 3
- [RA: projects where all used bolts size 6](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-projects-all-used-bolts) — Database Management System, chapter 3
- [RA: parts used in DBMS and MIS](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-parts-both-dbms-mis) — Database Management System, chapter 3
- [RA: computer dept employees and supervisors](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-computer-emp-supervisor) — Database Management System, chapter 3
- [RA: employees on Network over 15 hours](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-network-project-15-hours) — Database Management System, chapter 3