Basic Operators in Relational Algebra

Relational Algebra is a procedural query language, it is used to provide a single table / relation as output of performing operations on more than one relations. Some of the basic relations will be discussed here.

In our course of learning, we will use three relations (table) −

Table 1: course

Course_id	Name
1	Computer science
2	Information Technology
3	mechanical

Table 2: students

Roll No.	Name	address	age
1	Ram	Delhi	18
2	Raju	hyderabad	20
4	Faiz	Delhi	22
5	Salman	hyderabad	20

Table 3: Hostel

St. No.	Name	address	age
1	Ram	Delhi	18
2	Akash	hyderabad	20
3	neha	Jhansi	21

On this relations, we will perform some operation to make new relation based on operations performed.

• Selection operation (σ) − The selection operator denoted by sigma σ is used to select the tuples of a relation based on some condition. Only those tuples that fall under certain conditions are selected.

Syntax

σ(condition)(relation_name)

Example

Select the student with course id 1.
σ(course_id = 1)(student)

Result

Roll No.	Name	address	age
4	Faiz	Delhi	22

• Projection operation (∏) The projection operator denoted by ∏ is used to select columns from a specific reaction. Only specific columns are selected.

Syntax

∏(column1 , column2 , … , columnn)(relation_name)

Example

Let’s select all students's name and no who are in hostel.
∏( st. No. , name)(hostel)

Result

St. No.	Name
1	Ram
2	Akash
3	neha

The row are always distinct in projection i.e. if their is any other student whose name is panjak the other one is removed.

• Cross Product(X) - Cross product is denoted using the X symbol and is used to find the value of join of two variables. In cross product each tuple of relation1 is crossed with each tuple of relation2. Which makes the output relation of the order nXm, where n is the number of tuples in relation1 and m is the number of tuples in relation2.

Syntax

relation1 X relation2

Example

Let’s find cross product of course and hostel table.

student X course

St. No.	Name	address	age	Course_id	Name
1	Ram	Delhi	18	1	Computer science
1	Ram	Delhi	18	2	Information Technology
1	Ram	Delhi	18	3	mechanical
2	Akash	hyderabad	20	1	Computer science
2	Akash	hyderabad	20	2	Information Technology
2	Akash	hyderabad	20	3	mechanical
3	neha	Jhansi	21	1	Computer science
3	neha	Jhansi	21	2	Information Technology
3	neha	Jhansi	21	3	mechanical

• Union (U) - The union of two relations relation1 and relation2 will gives the tuples that are either in relation1 or in relation2 but tuples that are in both relation1 and relation2 are considered only once.

  Also both relations should be of the same domain for finding there union.

Syntax

relation1 U relation2

Example

Let’s find the union of student and hostel

student U hostel

Roll No.	Name	address	age
1	Ram	Delhi	18
2	Raju	hyderabad	20
4	Faiz	Delhi	22
5	Salman	hyderabad	20
2	Akash	hyderabad	20
3	neha	Jhansi	21

• Minus (-) operator - operator is denoted by - symbol. Relation1 - relation2 will result into a relation in which the tuple in relation1 and not in relation2 are present. For calculating minus too, the relations must be union compatible.

Syntax

relation1 - relation2

Example

Let’s find the operation student - hostel

student - hostel

Roll No.	Name	address	age
2	Raju	hyderabad	20
4	Faiz	Delhi	22
5	Salman	hyderabad	20

• rename(ρ) − the rename operation denoted by the ρ is used to rename the given relation to another name given.

Syntax

ρ(new_name , old_name)