Chapter 3: Relational Algebra and Relational Calculus

Relational Algebra is more operational and is useful for representing execution plans.

Relational Calculus is non-operational and lets the user describe what they want instead of how to compute it.

Relational Algebra

An algebra is a formal language consisting of sets and their operations.

Operations of relational algebra can be divided into two groups:

• Set operations like UNION, INTERSECTION, SET DIFFERENCE, CROSS PRODUCT.
• Relational database specific operations like SELECT, PROJECT, JOIN.

Set Operations on Relations

• Union Operation: includes all tuples that appear in R1, R2 or both where R1 and R2 are relations.
  • For R1 and R2 to be union compatible they should meet the following conditions:
    • R1 and R2 must have the same number of attributes.
    • Each corresponding pair of attributes must have the same domain.
    • Duplicate tuples are automatically eliminated.
• Intersection Operation: includes all tuples that appear in both R1 and R2.
  • For R1 and R2 to be intersection compatible they should be union compatible.
• Set Difference: includes all tuples that are an element of R1 but not R2 for R1 - R2.
  • For R1 and R2 to be difference compatible they should be union compatible.
• Cartesian Product: includes all tuples that result from the cross product of R1 and R2.
  • If R1 has n attributes and R2 has m attributes their cross product will have n * m attributes.
  • R1 and R2 don’t have to be union compatible.

Fundamental Operations

• Projection Operation: displays a subset of attributes of a table.

  • Duplication rows are automatically eliminated.

  

• Select Operation: select a subset of tuples based on the selection condition.

  

To select the attributes subject and author from a Books relation we would use:

To select books where the subject is database and the price is 450 we would use: