---
title: "RA: employees on Network over 15 hours"
subject: "Database Management System"
chapter: 3
key: "semester_6/database_management_system:ra-network-project-15-hours"
source: https://www.bctengineer.com/q/semester_6/database_management_system/ra-network-project-15-hours
site: BCT Engineering
---

# RA: employees on Network over 15 hours

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-network-project-15-hours
- Whole chapter: https://www.bctengineer.com/md/semester_6/database_management_system/chapter-3

## Question

Consider the relational schema:
emp (eid, name, add, sup_eid)
dep (dep_id, name)
project (pid, title, dep_id)
work (eid, pid, hours)
Find name of all employees who work on "Network" project for more than 15 hours. (Write a relational algebra expression.)

## Short answer

Select the Network project, join with work, keep hours greater than 15, join with emp, then project name. Expression: π name ( emp ⋈ σ hours > 15 ( work ⋈ σ title = "Network" (project) ) ).

## Answer

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

#### Relational algebra expression
```text
π name ( emp ⋈ σ hours > 15 ( work ⋈ σ title = "Network" (project) ) )
```

#### Explanation
1. σ title = "Network" (project) selects the Network project.
2. Joining with work on pid gives all work tuples of that project.
3. σ hours > 15 keeps only the tuples where the employee worked more than 15 hours.
4. Joining with emp on eid brings in the employee, and π name prints the names.

The expression is correct because emp and work share only eid, and work and project share only pid, so each natural join matches on the intended attribute.

#### Equivalent SQL (tested)
```sql
SELECT DISTINCT e.name
FROM emp e JOIN work w ON e.eid = w.eid
           JOIN project p ON p.pid = w.pid
WHERE p.title = 'Network' AND w.hours > 15;
```

## Check yourself

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

1. Which selections are used?
   A. σ hours>15 on project
   B. σ title=Network on project and σ hours>15 on work tuples
   C. σ title=Network on emp
   D. Only one on emp
   Answer: B. title is in project and hours in work. (Key point: Selections)

2. Why are the natural joins correct?
   A. All share name
   B. They share all attributes
   C. Natural join needs a condition
   D. emp and work share only eid; work and project share only pid
   Answer: D. Only the intended attributes match. (Key point: Natural join safety)

3. What does the final π name do?
   A. Filters hours
   B. Outputs only employee names
   C. Joins emp
   D. Deletes duplicates manually
   Answer: B. Projection chooses columns. (Key point: Projection)

## Related in Database Management System

- [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: delete Electrical dept projects](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-delete-electrical-projects) — Database Management System, chapter 3
- [RA: projects count per department](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-projects-per-department) — Database Management System, chapter 3
- [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
- [RA: employees on no project](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Ara-emp-no-project) — 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

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