Introduction

The Selection operation (denoted by σ) is a fundamental operation in relational algebra. It allows filtering of rows (or tuples) from a table based on specified conditions, resulting in horizontal partitioning.

Syntax of Selection

The general syntax for the selection operation is:

σ(condition)(Relation)

Conditions can include:

• Comparisons with constants (e.g., salary > 50000).
• Comparisons between attributes (e.g., dept_id = manager_id).
• Boolean Connectives (e.g., AND, OR).

Key Characteristics

• Horizontal Partitioning: Filters rows while preserving all columns.
• Commutativity: The order of conditions does not affect the final result.
• Combining Conditions: Multiple conditions can be combined using Boolean operators.

Examples

Example 1: Basic Selection

Given the Employee table:

emp_id | name   | dept_id | salary
101    | Alice  | 1       | 12000
102    | Bob    | 3       | 15000
103    | Carol  | 2       | 10000

Query: Select all employees in department 3.

σ(dept_id = 3)(Employee)

Result:

emp_id | name   | dept_id | salary
102    | Bob    | 3       | 15000

Example 2: Combining Conditions

Query: Select employees in department 1 with a salary greater than 10,000.

σ(dept_id = 1 ∧ salary > 10000)(Employee)

Result:

emp_id | name   | dept_id | salary
101    | Alice  | 1       | 12000

Advanced Concepts

Nested Selection

Due to commutativity, conditions can be applied in any order. For example:

• Step 1: Apply salary > 10000.
• Step 2: Apply dept_id = 1.

Attribute Comparison

Conditions can also compare attributes within the same tuple. For example:

σ(emp_id > dept_id)(Employee)

Applications

The selection operation is fundamental to SQL and forms the basis for query optimization in relational databases. It is essential for competitive exams like GATE and UGC NET.