This Document contains the description regarding "Relational Algebra".It provides operations that can be performed with it as well as Selection and Projection Queries.

1. by
Milap Bhanderi
Subject: Database Management System (DBMS)
Institute: Silver Oak College of Engineering and Technology.
Copyright © 2017 by Milap Bhanderi

2. What is Relational Algebra?
v Relational Algebra is formal description of how relational
database operates.
v It is a procedural query language, i.e. user must define
both “how” and “what” to retrieve.
v It consists of a set of operators that consume either one
or two relations as input. An operator produces one
relation as its output.
Copyright © 2017 by Milap Bhanderi

3. Introduction to Relational Algebra
• Introduced by E. F.
Codd in 1970.
• Codd proposed such
an algebra as a basis
for database query
languages.
Copyright © 2017 by Milap Bhanderi

4. Algebra Operations
• Unary Operations - operate on one relation. These
include select, project and rename operators.
• Binary Operations - operate on pairs of relations.
These include union, set difference, division,
cartesian product, equality join, natural join, join
and semi-join operators.
Copyright © 2017 by Milap Bhanderi

5. Select Operator
• The Select operator selects tuples that satisfies a predicate;
e.g. retrieve the employees whose salary is 30,000
σSalary = 30,000 (Employee)
• Conditions in Selection:
Simple Condition: (attribute)(comparison)(attribute)
(attribute)(comparison)(constant)
Comparison: =,≠,≤,≥,<,>
Condition: combination of simple conditions with AND, OR,
NOT Copyright © 2017 by Milap Bhanderi

6. Select Operator Example
Name Age Weight
Harry 34 80
Sally 28 64
George 29 70
Helena 54 54
Peter 34 80
Name Age Weight
Harry 34 80
Helena 54 54
Peter 34 80
Name Age Weight
Helena 54 54
Person σAge≥34(Person)
σAge=Weight(Person)
Copyright © 2017 by Milap Bhanderi

7. Project Operator
• Project (∏) retrieves a column. Duplication is
not permitted.
• e.g., name of employees:
∏ name(Employee)
e.g., name of employees earning more than
80,000:
∏ name(σSalary>80,000(Employee))
Copyright © 2017 by Milap Bhanderi

8. Project Operator Example
Name Age Salary
Harry 34 80,000
Sally 28 90,000
George 29 70,000
Helena 54 54,280
Peter 34 40,000
Name
Harry
Sally
George
Helena
Peter
Employee
∏ name(Employee)
Copyright © 2017 by Milap Bhanderi

9. Project Operator Example
Name Age Salary
Harry 34 80,000
Sally 28 90,000
George 29 70,000
Helena 54 54,280
Peter 34 40,000
Name
Sally
Name Age Salary
Sally 28 90,000
Employee σSalary>80,000(Employee)
∏ name(σSalary>80,000(Employee))
Copyright © 2017 by Milap Bhanderi

10. Rename Operator
• In relational algebra, a Rename is a unary operation written
as ρ a / b (R) where:
a and b are attribute names
R is a relation
• The result is identical to R except that the b field in all tuples
is renamed to an a field.
• Example, rename operator changes the name of its input
table to its subscript,
• ρ employee(Employee)
• Changes the name of Employee table to employee
Copyright © 2017 by Milap Bhanderi

11. Rename Operator Example
Name Salary
Harry 80,000
Sally 90,000
George 70,000
Helena 54,280
Peter 40,000
Emp_Name Salary
Harry 80,000
Sally 90,000
George 70,000
Helena 54,280
Peter 40,000
Employee ρ Emp_Name / Name (Employee)
Copyright © 2017 by Milap Bhanderi

12. Copyright © 2017 by Milap Bhanderi