Basic Operators in Relational Algebra

Basics of Relational model: Relational Model

Relational Algebra is a procedural query language that takes relations as an input and returns relations as an output. There are some basic operators which can be applied in relation to producing the required results which we will discuss one by one. We will use STUDENT_SPORTS, EMPLOYEE, and STUDENT relations as given in Table 1, Table 2, and Table 3 respectively to understand the various operators. 

Table 1: STUDENT_SPORTS

ROLL_NO	SPORTS
1	Badminton
2	Cricket
2	Badminton
4	Badminton

Table 2: EMPLOYEE

EMP_NO	NAME	ADDRESS	PHONE	AGE
1	RAM	DELHI	9455123451	18
5	NARESH	HISAR	9782918192	22
6	SWETA	RANCHI	9852617621	21
4	SURESH	DELHI	9156768971	18

Table 3: STUDENT

ROLL_NO	NAME	ADDRESS	PHONE	AGE
1	RAM	DELHI	9455123451	18
2	RAMESH	GURGAON	9652431543	18
3	SUJIT	ROHTAK	9156253131	20
4	SURESH	DELHI	9156768971	18

Selection operator (σ): Selection operator is used to selecting tuples from a relation based on some condition. Syntax: 

σ (Cond)(Relation Name)

Extract students whose age is greater than 18 from STUDENT relation given in Table 3  

σ (AGE>18)(STUDENT)

[Note: SELECT operator does not show any result, the projection operator must be called before the selection operator to generate or project the result. So, the correct syntax to generate the result is: ∏(σ (AGE>18)(STUDENT))]

RESULT:

ROLL_NO	NAME	ADDRESS	PHONE	AGE
3	SUJIT	ROHTAK	9156253131	20

Projection Operator (∏): Projection operator is used to project particular columns from a relation. Syntax:  

∏(Column 1,Column 2….Column n)(Relation Name)

Extract ROLL_NO and NAME from STUDENT relation given in Table 3  

∏(ROLL_NO,NAME)(STUDENT)

RESULT:

ROLL_NO	NAME
1	RAM
2	RAMESH
3	SUJIT
4	SURESH

Note: If the resultant relation after projection has duplicate rows, it will be removed. For Example  ∏_(ADDRESS)(STUDENT) will remove one duplicate row with the value DELHI and return three rows. 

Cross Product(X): Cross product is used to join two relations. For every row of Relation1, each row of Relation2 is concatenated. If Relation1 has m tuples and and Relation2 has n tuples, cross product of Relation1 and Relation2 will have m X n tuples. Syntax: 

Relation1 X Relation2

To apply Cross Product on STUDENT relation given in Table 1 and STUDENT_SPORTS relation given in Table 2,  

STUDENT X STUDENT_SPORTS

RESULT:

ROLL_NO	NAME	ADDRESS	PHONE	AGE	ROLL_NO	SPORTS
1	RAM	DELHI	9455123451	18	1	Badminton
1	RAM	DELHI	9455123451	18	2	Cricket
1	RAM	DELHI	9455123451	18	2	Badminton
1	RAM	DELHI	9455123451	18	4	Badminton
2	RAMESH	GURGAON	9652431543	18	1	Badminton
2	RAMESH	GURGAON	9652431543	18	2	Cricket
2	RAMESH	GURGAON	9652431543	18	2	Badminton
2	RAMESH	GURGAON	9652431543	18	4	Badminton
3	SUJIT	ROHTAK	9156253131	20	1	Badminton
3	SUJIT	ROHTAK	9156253131	20	2	Cricket
3	SUJIT	ROHTAK	9156253131	20	2	Badminton
3	SUJIT	ROHTAK	9156253131	20	4	Badminton
4	SURESH	DELHI	9156768971	18	1	Badminton
4	SURESH	DELHI	9156768971	18	2	Cricket
4	SURESH	DELHI	9156768971	18	2	Badminton
4	SURESH	DELHI	9156768971	18	4	Badminton

Union (U): Union on two relations R1 and R2 can only be computed if R1 and R2 are union compatible (These two relations should have the same number of attributes and corresponding attributes in two relations have the same domain). Union operator when applied on two relations R1 and R2 will give a relation with tuples that are either in R1 or in R2. The tuples which are in both R1 and R2 will appear only once in the result relation. Syntax: 

 Relation1 U Relation2

Find the person who is either student or employees, we can use Union operators like: 

STUDENT U EMPLOYEE

RESULT:

ROLL_NO	NAME	ADDRESS	PHONE	AGE
1	RAM	DELHI	9455123451	18
2	RAMESH	GURGAON	9652431543	18
3	SUJIT	ROHTAK	9156253131	20
4	SURESH	DELHI	9156768971	18
5	NARESH	HISAR	9782918192	22
6	SWETA	RANCHI	9852617621	21

Minus (-): Minus on two relations R1 and R2 can only be computed if R1 and R2 are union compatible. Minus operator when applied on two relations as R1-R2 will give a relation with tuples that are in R1 but not in R2. Syntax: 

 Relation1 - Relation2

Find the person who is a student but not an employee, we can use minus operator like:  

STUDENT - EMPLOYEE

RESULT:

ROLL_NO	NAME	ADDRESS	PHONE	AGE
2	RAMESH	GURGAON	9652431543	18
3	SUJIT	ROHTAK	9156253131	20

Rename(ρ): Rename operator is used to giving another name to a relation. Syntax:  

ρ(Relation2, Relation1)

To rename STUDENT relation to STUDENT1, we can use rename operator like:  

ρ(STUDENT1, STUDENT)

If you want to create a relation STUDENT_NAMES with ROLL_NO and NAME from STUDENT, it can be done using rename operator as:  

ρ(STUDENT_NAMES, ∏(ROLL_NO, NAME)(STUDENT))

Extended Relational Algebra Operators Overview of Relational Algebra Operators

Previous Year Gate Questions 
https://www.geeksforgeeks.org/gate-gate-cs-2012-question-50/
https://www.geeksforgeeks.org/gate-gate-cs-2012-question-43/

Article contributed by Sonal Tuteja. Please write comments if you find anything incorrect, or if you want to share more information about the topic discussed above.