Relational Algebra – Selection Operation (σ) in DBMS

Relational Algebra Operations – Selection (σ)

In the Relational Algebra of DBMS, the Selection Operation is used to extract specific rows (tuples) from a relation (table) that satisfy a given condition. It acts as a filtering operation, similar to the WHERE clause in SQL.

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🔹 Definition

The Selection operation is a unary operation (applies on a single relation). It selects those rows that satisfy a specified predicate or condition.

Notation:

σcondition(Relation_Name)

Here, σ (sigma) denotes the selection operator, and the subscript specifies the condition.

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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: Selecting Students from Dhaka

Operation:

σDistrict = 'Dhaka'(Student)

Result:

Student_ID	Name	Age	Department	District
101	Rafi Ahmed	22	CSE	Dhaka
104	Sumaiya Akter	20	BBA	Dhaka

Explanation: Only those tuples where District = 'Dhaka' are selected.

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🟩 Example 2: Selecting CSE Students Aged Over 22

Operation:

σDepartment = 'CSE' AND Age > 22(Student)

Result:

Student_ID	Name	Age	Department	District
105	Imran Hossain	24	CSE	Chattogram

Explanation: The query selects only students from the CSE department whose age is greater than 22.

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🔹 Common Selection Conditions

• Comparison: <, <=, >, >=, =, ≠
• Logical Operators: AND (∧), OR (∨), NOT (¬)
• Range Condition: BETWEEN, IN, etc.

Examples:

• σ_{Age > 21}(Student)
• σ_{Department = 'EEE' OR Department = 'CSE'}(Student)
• σ_{District ≠ 'Dhaka'}(Student)

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🔹 Key Properties

• Selection is a filtering operation — it does not alter columns, only filters rows.
• The output relation has the same attributes as the input relation.
• It can be combined with other operations like projection and join for complex queries.

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✅ Summary

Feature	Description
Operator	σ (Sigma)
Purpose	Selects tuples that satisfy a condition
Input	One relation
Output	Subset of rows of the same relation
SQL Equivalent	SELECT * FROM table WHERE condition;

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