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
 Union Operator (∪)
 Intersection Operator (∩)
 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

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 
Relation R ∪ S
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 
Relation R ∩ S
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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