Which of the following is not a relational algebra function

Relational algebra is a formal system for manipulating relations, which are mathematical abstractions representing tables of data. It provides a set of operations to manipulate these relations, such as selection, projection, union, intersection, and difference. However, not all operations on relations are part of the relational algebra. In this blog, we will discuss which of the following is not a relational algebra function with an example in detail. The following are the five basic operations of the relational algebra:

1. Selection: This operation selects a subset of rows from a relation that satisfies a given condition. The condition is expressed as a Boolean expression that evaluates to true or false for each row in the relation.

For example, consider the following relation:

Student(Name, Age, Gender, GPA)

To select all female students, we can use the selection operation as follows:

σ(Gender = 'F')(Student)

This will return a new relation that contains only the rows where the Gender attribute is equal to ‘F’.

2. Projection: This operation selects a subset of columns from a relation. It returns a new relation that contains only the selected columns.

For example, consider the following relation:

Student(Name, Age, Gender, GPA)

To project only the Name and GPA columns, we can use the projection operation as follows:

π(Name, GPA)(Student)

This will return a new relation that contains only the Name and GPA columns.

3. Union: This operation combines two relations into a single relation that contains all the rows from both relations. Duplicate rows are eliminated.

For example, consider the following two relations:

R(A, B)
S(A, B)

To combine these two relations, we can use the union operation as follows:

R ∪ S

This will return a new relation that contains all the rows from both R and S, with duplicate rows eliminated.

4. Intersection: This operation returns a relation that contains only the rows that appear in both of the input relations.

For example, consider the following two relations:

R(A, B)
S(A, B)

To find the rows that appear in both R and S, we can use the intersection operation as follows:

R ∩ S

This will return a new relation that contains only the rows that appear in both R and S.

5. Difference: This operation returns a relation that contains only the rows that appear in the first input relation but not in the second input relation.

For example, consider the following two relations:

R(A, B)
S(A, B)

To find the rows that appear in R but not in S, we can use the difference operation as follows:

R - S

This will return a new relation that contains only the rows that appear in R but not in S. All of the above operations are part of the relational algebra. However, the following operation is not part of the relational algebra:

1. Join: This operation combines two relations into a single relation by matching the values of a common attribute. There are several types of joins, such as inner join, outer join, left join, and right join. Although joins are commonly used in database systems, they are not part of the basic relational algebra.

For example, consider the following two relations:

Student(Name, Age, Gender, GPA)
Course(Name, Code, Instructor)

To join these two relations on the Name attribute, we can use the join operation as follows:

Student ⋈ Course

This will return a new relation that contains all the rows from both Student and Course where the Name attribute matches. In conclusion, the join operation is not a basic operation of relational algebra. While it is commonly used in database systems, it is not part of the formal system of manipulating relations. The five basic operations of relational algebra are selection, projection, union, intersection, and difference.