Introduction
Relational Algebra was developed before the SQL. It is a procedural query language. Relational algebra received little attention outside of pure mathematics until the publication of E.F.Codd’s relational model of data in 1970. Codd proposed such an algebra as a basis for database query languages.
There a five primitive operators in Codd’s algebra.
selection
projection
Cartesian product
set union
set difference
Relational algebra is divided into several groups:
Unary Relational Operation
SELECT,PROJECT,RENAME
Relational oparetions algebra form Set Theory
UNION,INTERSECTION,MINUS,CARTESIAN PRODUCT
Binary Relational Operation
JOIN,DEVISION
Unary Relational Operation
Select operation(σ)
This operation is used to select a subset of tuples in a relation which satisfies a selection condition. This produces horizontal subset of table.
Syntax:
σ <condition> (R)
Example:
Select all the details of the students in class
σ ClassID=C003 (Student)
Project Operation(π)
This operation selects specified columns in the table and delete other columns. This produces vertical subsets of table and remove duplicate tuples
Syntax:
π <attribute list> (R)
Example:
Select ID and Name column from the Student table
σ ID,Name (Student)
Rename Operation
This operation allows us to rename output relations
notation:
ρs(R)
Union Operation(∪)
This performs binary union between two given relations.
notation:
R ∪ S Example:
Select ID and Name of all the students and ClassID and ClassName of the all classes.
Student ∪ Class
This is same as:
SELECT Student.*,Class.* FROM Student,Class;
Intersection Operation(⋂)
This defines a relation consisting of the set of all the tuples that are both in R and S .
notation:
R ⋂ S 
Example:
Select all the student that have cars.
Student ⋂ CarOwn
This is same as:
SELECT Student.*,CarOwn.* FROM Student,CarOwn where Student.ID=CarOwn.ID;
Minus or Set Difference Operation
This defines as R – S. This is a relation that includes all the tuples that are in R but not in S .
notation:
R - S 
Example:
Select all the student that don’t have cars.
Student – CarOwn
This is same as:
SELECT* FROM Student where Student.ID not in (CarOwn.ID);
Cartesian Product Operation
This defines a relation that is the concatenation of all the tuples of R and all the tuples of S.
notation:
R × S 
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