## Relational Algebra Operators-

Before you go through this article, make sure that you have gone through the previous article on Introduction to Relational Algebra.

The operators in relational algebra are classified as-

In this article, we will discuss about Set Theory Operators.

## Set Theory Operators-

Following operators are called as set theory operators-

1. Union Operator (∪)
2. Intersection Operator (∩)
3. Difference Operator (-)

### Condition For Using Set Theory Operators

To use set theory operators on two relations,

The two relations must be union compatible.

Union compatible property means-

• Both the relations must have same number of attributes.
• The attribute domains (types of values accepted by attributes) of both the relations must be compatible.

Also read- Selection Operator and Projection Operator

## 1. Union Operator (∪)-

Let R and S be two relations.

Then-

• R ∪ S is the set of all tuples belonging to either R or S or both.
• In R ∪ S, duplicates are automatically removed.
• Union operation is both commutative and associative.

## Example-

Consider the following two relations R and S-

 ID Name Subject 100 Ankit English 200 Pooja Maths 300 Komal Science

#### Relation R

 ID Name Subject 100 Ankit English 400 Kajol French

#### Relation S

Then, R ∪ S is-

 ID Name Subject 100 Ankit English 200 Pooja Maths 300 Komal Science 400 Kajol French

## 2. Intersection Operator (∩)-

Let R and S be two relations.

Then-

• R ∩ S is the set of all tuples belonging to both R and S.
• In R ∩ S, duplicates are automatically removed.
• Intersection operation is both commutative and associative.

## Example-

Consider the following two relations R and S-

 ID Name Subject 100 Ankit English 200 Pooja Maths 300 Komal Science

#### Relation R

 ID Name Subject 100 Ankit English 400 Kajol French

#### Relation S

Then, R ∩ S is-

 ID Name Subject 100 Ankit English

## 3. Difference Operator (-)-

Let R and S be two relations.

Then-

• R – S is the set of all tuples belonging to R and not to S.
• In R – S, duplicates are automatically removed.
• Difference operation is associative but not commutative.

### Example-

Consider the following two relations R and S-

 ID Name Subject 100 Ankit English 200 Pooja Maths 300 Komal Science

#### Relation R

 ID Name Subject 100 Ankit English 400 Kajol French

#### Relation S

Then, R – S is-

 ID Name Subject 200 Pooja Maths 300 Komal Science

#### Relation R – S

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