**The Relational Algebra and Relational Calculus**

List the operations of relational algebra and the purpose of each.

8.2. What is union compatibility? Why do the UNION, INTERSECTION, and

DIFFERENCE operations require that the relations on which they are applied be union compatible?

8.3. Discuss some types of queries for which renaming of attributes is necessary in order to specify the query unambiguously.

8.4. Discuss the various types of inner join operations. Why is theta join required?

8.5. What role does the concept of foreign key play when specifying the most common types of meaningful join operations?

8.6. What is the FUNCTION operation? For what is it used?

8.7. How are the OUTER JOIN operations different from the INNER JOIN opera- tions? How is the OUTER UNION operation different from UNION?

8.8. In what sense does relational calculus differ from relational algebra, and in what sense are they similar?

8.9. How does tuple relational calculus differ from domain relational calculus?

8.10. Discuss the meanings of the existential quantifier (∃) and the universal quantifier (∀).

8.11. Define the following terms with respect to the tuple calculus: tuple variable, range relation, atom, formula, and expression.

8.12. Define the following terms with respect to the domain calculus: domain variable, range relation, atom, formula, and expression.

8.13. What is meant by a safe expression in relational calculus?

8.14. When is a query language called relationally complete?