# Explain division operation in relational algebra (DBMS)?

DBMSDatabaseBig Data Analytics

Query is a question or requesting information. Query language is a language which is used to retrieve information from a database.

Query language is divided into two types −

• Procedural language

• Non-procedural language

## Procedural language

Information is retrieved from the database by specifying the sequence of operations to be performed.

For Example: Relational algebra.

Structure Query language (SQL) is based on relational algebra.

Relational algebra consists of a set of operations that take one or two relations as an input and produces a new relation as output.

### Types of Relational Algebra operations

The different types of relational algebra operations are as follows −

• Select operation

• Project operation

• Rename operation

• Union operation

• Intersection operation

• Difference operation

• Cartesian product operation

• Join operation

• Division operation

Union, intersection, difference, cartesian, join, division comes under binary operation (operate on two table).

## Division operation

The division operator is used for queries which involve the ‘all’.

R1 ÷ R2 = tuples of R1 associated with all tuples of R2.

### Example

Retrieve the name of the subject that is taught in all courses.

NameCourse
SystemBtech
DatabaseMtech
DatabaseBtech
AlgebraBtech

÷

Course
Btech
Mtech

=

 Name database

The resulting operation must have all combinations of tuples of relation S that are present in the first relation or R.

### Example

Retrieve names of employees who work on all the projects that John Smith works on.

Consider the Employee table given below −

NameEnoPno
John123P1
Smith123P2
A121P3

÷

Works on the following −

EnoPnoPname
123P1Market
123P2Sales

=

The result is as follows

Eno
123

The expression is as follows

Smith <- ΠPno(σEname = ‘john smith’ (employee * works on Pno=Eno))
Published on 06-Jul-2021 14:44:58