# Explain intersection 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 tables).

## Intersection operation

It displays the common values in R1 & R2. It is denoted by ∩.

### Syntax

∏regno(R1) ∩ ∏regno(R2)

Consider two sets,

A={1,2,4,6} and B={1,2,7}

Intersection of A and B

A ∩ B ={1,2}

Elements that are present in both sets A and B are present in the set obtained by intersection of A and B.

In relational algebra if R1 and R2 are two instances of relation then,

R1 ∩ R2 ={ x | x€ R1 and x € R2}

That is, the intersection of R1 and R2 only those tuples will be present that are in both R1 and R2

### Example

Find all the customers whose account is in the bank and have taken out a loan.

The expression is as follows −

∏Name(Depositor) ∩ ∏Name(Borrower)

IDName
1A
2B
3C

### Borrower

IDName
2B
3A
5D

So, the intersection of depositor and borrower is as follows −

 A B
Published on 06-Jul-2021 14:25:01