Introduction to Relational Algebra

Relational Algebra is a procedural query language used to retrieve and manipulate data stored in a relational database. It forms the theoretical backbone of SQL and provides a robust framework for query optimization and database design.

Key Operations in Relational Algebra

• Selection (σ): Filters rows based on a specified condition.
• Projection (π): Selects specific columns, eliminating duplicates.
• Union (∪): Combines two relations and removes duplicates.
• Set Difference (−): Returns rows in one relation but not in another.
• Cartesian Product (×): Combines every row of one relation with every row of another.
• Natural Join (⨝): Combines two relations based on common attributes.
• Division (÷): Used for queries involving “all conditions.”

Examples

Selection

Find employees with a salary greater than 50,000.

σ(salary > 50000)(Employee)

Projection

Retrieve the Name and Salary columns of employees.

π(Name, Salary)(Employee)

Join

Combine Employee and Department based on department ID.

Employee ⨝ (Employee.dept_id = Department.dept_id) Department

Relational Calculus

Relational Calculus is a declarative query language. It emphasizes what data to retrieve without specifying how to retrieve it. There are two forms:

• Tuple Relational Calculus (TRC): Works with tuples.
• Domain Relational Calculus (DRC): Works with domains of attributes.

GATE and UGC NET Focus

Both Relational Algebra and Relational Calculus are crucial topics for database-related questions in GATE and UGC NET exams. Example questions often involve forming queries using algebraic operations or evaluating their results.

Sample GATE Question

Question: Find students scoring above 75 marks using Relational Algebra.

σ(marks > 75)(Student)