Relational Algebra – Projection (π) Operation in DBMS

Relational Algebra Operations – Projection (π)

In Relational Algebra, the Projection Operation is used to select specific columns (attributes) from a relation (table). It eliminates unwanted attributes and displays only the required information. Projection is similar to the SELECT column_list clause in SQL.

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🔹 Definition

The Projection operation is a unary operation (works on a single relation). It selects only the specified attributes and removes duplicates automatically (if any).

Notation:

πattribute_list(Relation_Name)

Here, π (pi) denotes the projection operator, and the subscript lists the attributes (columns) you want to display.

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🔹 Example (Bangladeshi Context)

Consider the following relation Student:

Student_ID	Name	Age	Department	District
101	Rafi Ahmed	22	CSE	Dhaka
102	Shanta Rahman	21	EEE	Khulna
103	Tanvir Hasan	23	CSE	Rajshahi
104	Sumaiya Akter	20	BBA	Dhaka
105	Imran Hossain	24	CSE	Chattogram

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🟩 Example 1: Displaying Only Name and Department

Operation:

πName, Department(Student)

Result:

Name	Department
Rafi Ahmed	CSE
Shanta Rahman	EEE
Tanvir Hasan	CSE
Sumaiya Akter	BBA
Imran Hossain	CSE

Explanation: Only the columns Name and Department are projected (displayed).

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🟩 Example 2: Displaying Unique Department Names

Operation:

πDepartment(Student)

Result:

Department
CSE
EEE
BBA

Explanation: The projection removes duplicate department values automatically.

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🟩 Example 3: Displaying Name and District of CSE Students

Combined Operation:

πName, District(σDepartment='CSE'(Student))

Result:

Name	District
Rafi Ahmed	Dhaka
Tanvir Hasan	Rajshahi
Imran Hossain	Chattogram

Explanation: First, the selection (σ) filters CSE students, then projection (π) extracts only Name and District.

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🔹 Properties of Projection

• Projection extracts only the specified columns.
• It automatically removes duplicate rows (sets are unordered and unique).
• It is often used with Selection for complex queries.

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🔹 SQL Equivalent

SELECT Name, Department FROM Student;
SELECT DISTINCT Department FROM Student;

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✅ Summary Table

Feature	Description
Operator	π (Pi)
Purpose	Select specific attributes (columns)
Input	One relation
Output	Subset of columns from the same relation
SQL Equivalent	SELECT column_list FROM table;

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🔹 Real-Life Use (Bangladesh Example)

In a university database in Bangladesh, projection can be used to:

• Display only Student Names and Districts for admission records.
• List unique departments available at Dhaka University.
• Generate a report of names and departments for final year CSE students.

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