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# Basic Operators in Relational Algebra

Basics of Relational model: Relational Model

Relational Algebra is a procedural query language that takes relations as an input and returns relations as an output. There are some basic operators which can be applied in relation to producing the required results which we will discuss one by one. We will use STUDENT_SPORTS, EMPLOYEE, and STUDENT relations as given in Table 1, Table 2, and Table 3 respectively to understand the various operators.

Table 1: STUDENT_SPORTS

Table 2: EMPLOYEE

Table 3: STUDENT

Selection operator (σ): Selection operator is used to selecting tuples from a relation based on some condition. Syntax:

`σ (Cond)(Relation Name)`

Extract students whose age is greater than 18 from STUDENT relation given in Table 3

`σ (AGE>18)(STUDENT)`

[Note: SELECT operator does not show any result, the projection operator must be called before the selection operator to generate or project the result. So, the correct syntax to generate the result is: ∏(σ (AGE>18)(STUDENT))]

RESULT:

Projection Operator (∏): Projection operator is used to project particular columns from a relation. Syntax:

`∏(Column 1,Column 2….Column n)(Relation Name)`

Extract ROLL_NO and NAME from STUDENT relation given in Table 3

`∏(ROLL_NO,NAME)(STUDENT)`

RESULT:

Note: If the resultant relation after projection has duplicate rows, it will be removed. For Example  ∏(ADDRESS)(STUDENT) will remove one duplicate row with the value DELHI and return three rows.

Cross Product(X): Cross product is used to join two relations. For every row of Relation1, each row of Relation2 is concatenated. If Relation1 has m tuples and and Relation2 has n tuples, cross product of Relation1 and Relation2 will have m X n tuples. Syntax:

`Relation1 X Relation2`

To apply Cross Product on STUDENT relation given in Table 1 and STUDENT_SPORTS relation given in Table 2,

`STUDENT X STUDENT_SPORTS`

RESULT:

Union (U): Union on two relations R1 and R2 can only be computed if R1 and R2 are union compatible (These two relations should have the same number of attributes and corresponding attributes in two relations have the same domain). Union operator when applied on two relations R1 and R2 will give a relation with tuples that are either in R1 or in R2. The tuples which are in both R1 and R2 will appear only once in the result relation. Syntax:

` Relation1 U Relation2`

Find the person who is either student or employees, we can use Union operators like:

`STUDENT U EMPLOYEE`

RESULT:

Minus (-): Minus on two relations R1 and R2 can only be computed if R1 and R2 are union compatible. Minus operator when applied on two relations as R1-R2 will give a relation with tuples that are in R1 but not in R2. Syntax:

` Relation1 - Relation2`

Find the person who is a student but not an employee, we can use minus operator like:

`STUDENT - EMPLOYEE`

RESULT:

Rename(ρ): Rename operator is used to giving another name to a relation. Syntax:

`ρ(Relation2, Relation1)`

To rename STUDENT relation to STUDENT1, we can use rename operator like:

`ρ(STUDENT1, STUDENT)`

If you want to create a relation STUDENT_NAMES with ROLL_NO and NAME from STUDENT, it can be done using rename operator as:

`ρ(STUDENT_NAMES, ∏(ROLL_NO, NAME)(STUDENT))`