## 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-

## 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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## 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-

## Projection Operator-

• Projection Operator (π) is a unary operator in relational algebra that performs a projection operation.
• It displays the columns of a relation or table based on the specified attributes.

 π(R)

## Example-

Consider the following Student relation-

 ID Name Subject Age 100 Ashish Maths 19 200 Rahul Science 20 300 Naina Physics 20 400 Sameer Chemistry 21

Then, we have-

### Result for Query πName, Age(Student)-

 Name Age Ashish 19 Rahul 20 Naina 20 Sameer 21

### Result for Query πID , Name(Student)-

 ID Name 100 Ashish 200 Rahul 300 Naina 400 Sameer

## Point-01:

• The degree of output relation (number of columns present) is equal to the number of attributes mentioned in the attribute list.

## Point-02:

• Projection operator automatically removes all the duplicates while projecting the output relation.
• So, cardinality of the original relation and output relation may or may not be same.
• If there are no duplicates in the original relation, then the cardinality will remain same otherwise it will surely reduce.

## Point-03:

• If attribute list is a super key on relation R, then we will always get the same number of tuples in the output relation.
• This is because then there will be no duplicates to filter.

## Point-04:

• Projection operator does not obey commutative property i.e.

π <list2> (π <list1> (R)) ≠ π <list1> (π <list2> (R))

## Point-05:

• Following expressions are equivalent because both finally projects columns of list-1

π <list1> (π <list2> (R)) = π <list1> (R)

## Point-06:

• Selection Operator performs horizontal partitioning of the relation.
• Projection operator performs vertical partitioning of the relation.

## Point-07:

• There is only one difference between projection operator of relational algebra and SELECT operation of SQL.
• Projection operator does not allow duplicates while SELECT operation allows duplicates.
• To avoid duplicates in SQL, we use “distinct” keyword and write SELECT distinct.
• Thus, projection operator of relational algebra is equivalent to SELECT operation of SQL.

Next Article- Set Theory Operators in Relational Algebra

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## Relational Algebra-

 Relational Algebra is a procedural query language which takes a relation as an input and generates a relation as an output.

## Relational Algebra Operators-

The operators in relational algebra may be classified as-

We will discuss all these operators one by one in detail.

## Characteristics-

Following are the important characteristics of relational operators-

• Relational Operators always work on one or more relational tables.
• Relational Operators always produce another relational table.
• The table produced by a relational operator has all the properties of a relational model.

Next Article- Selection Operator in Relational Algebra

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