Basic Operators in Relational Algebra

• Difficulty Level : Easy
• Last Updated : 29 Jul, 2021

Basics of Relational model: Relational Model 

Relational Algebra is a procedural query language that takes relations as an input and returns relation as an output. There are some basic operators which can be applied on relations to produce 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_NOSPORTS1Badminton2Cricket2Badminton4Badminton

 Table 2: EMPLOYEE

EMP_NONAMEADDRESSPHONEAGE1RAMDELHI9455123451185NARESHHISAR9782918192226SWETARANCHI9852617621214SURESHDELHI915676897118

Table 3: STUDENT 

ROLL_NONAMEADDRESSPHONEAGE1RAMDELHI9455123451182RAMESHGURGAON9652431543183SUJITROHTAK9156253131204SURESHDELHI915676897118

Selection operator (σ): Selection operator is used to select 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)

RESULT: 

ROLL_NONAMEADDRESSPHONEAGE3SUJITROHTAK915625313120

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_NONAME1RAM2RAMESH3SUJIT4SURESH

Note: If resultant relation after projection has duplicate rows, it will be removed. For Example:  ∏(ADDRESS)(STUDENT) will remove one duplicate row with 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_NONAMEADDRESSPHONEAGEROLL_NOSPORTS1RAMDELHI9455123451181Badminton1RAMDELHI9455123451182Cricket1RAMDELHI9455123451182Badminton1RAMDELHI9455123451184Badminton2RAMESHGURGAON9652431543181Badminton2RAMESHGURGAON9652431543182Cricket2RAMESHGURGAON9652431543182Badminton2RAMESHGURGAON9652431543184Badminton3SUJITROHTAK9156253131201Badminton3SUJITROHTAK9156253131202Cricket3SUJITROHTAK9156253131202Badminton3SUJITROHTAK9156253131204Badminton4SURESHDELHI9156768971181Badminton4SURESHDELHI9156768971182Cricket4SURESHDELHI9156768971182Badminton4SURESHDELHI9156768971184Badminton

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

 Relation1 U Relation2

Find person who are either student or employee, we can use Union operator like: 

STUDENT U EMPLOYEE

RESULT:  

ROLL_NONAMEADDRESSPHONEAGE1RAMDELHI9455123451182RAMESHGURGAON9652431543183SUJITROHTAK9156253131204SURESHDELHI9156768971185NARESHHISAR9782918192226SWETARANCHI985261762121

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 which are in R1 but not in R2. Syntax: 

 Relation1 - Relation2

Find person who are student but not employee, we can use minus operator like:  

STUDENT - EMPLOYEE

RESULT:  

ROLL_NONAMEADDRESSPHONEAGE2RAMESHGURGAON9652431543183SUJITROHTAK915625313120

Rename(ρ): Rename operator is used to give 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))