1. Copyright © 2004 Pearson Education, Inc.

2. Chapter 6 The Relational Algebra and Relational Calculus

3. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-3 Unary Relational Operations: SELECT and PROJECT The SELECT Operation The PROJECT Operation Sequences of Operations and the RENAME Operation

4. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-4 Relational Algebra Operations from Set Theory The UNION, INTERSECTION, and MINUS Operations The CARTESIAN PRODUCT (or CROSS PRODUCT) Operation

5. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-5 Binary Relational Operations: JOIN and DIVISION The JOIN Operation The EQUIJOIN and NATURAL JOIN Variations of JOIN A Complete Set of Relational Algebra Operations The DIVISION Operation

6. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-6 Additional Relational Operations Aggregate Functions and Grouping Recursive Closure Operations OUTER JOIN Operations The OUTER JOIN Operation

7. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-7 Examples of Queries in Relational Algebra

8. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-8 The Tuple Relational Calculus Tuple Variables and Range Relations Expressions and Formulas in Tuple Relational Calculus The Existential and Universal Quantifiers Example Queries Using the Existential Quantifier Transforming the Universal and Existential Quantifiers Using the Universal Quantifier Safe Expressions

9. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-9 The Domain Relational Calculus

10. Elmasri and Navathe, Fundamentals of Database Systems, Fourth Edition Copyright © 2004 Pearson Education, Inc. Slide 6-10 Summary