Tamil Nadu Board of Secondary EducationHSC Science Class 12th

# Explain the different operators in Relational algebra with suitable examples. - Computer Science

Explain the different operators in Relational algebra with suitable examples.

#### Solution

Relational Algebra Operations from Set Theory

1. UNION (∪)
2. INTERSECTION (∩)
3. DIFFERENCE (-)
4. CARTESIAN PRODUCT (X)

SELECT (symbol: σ)

General form σ<sub>c</sub> ( R) with a relation R and a condition C on the attributes of R.
The SELECT operation is used for selecting a subset with tuples according to a given condition. Select filters out all tuples that do not satisfy C.

 Studno Name Course Year cs1 Kannan Big Data II cs2 Gowri Shankar R language I cs3 Lenin Big Data I cs4 Padmaja Python Programming I

PROJECT (symbol: II)
The projection eliminates all attributes of the input relation but those mentioned in the projection list.
Example 1 using Table A
π<sub>course</sub> (STUDENT)
Result

 Course Big Data R language Python Programming

Course Big Data R language PythonProgramming
Note: duplicate row is removed in the result UNION (Symbol: u)
It includes all tuples that are in tables A or in B. It also eliminates duplicates. Set A Union Set B would be expressed asAuB

Example 2:
Consider the following tables

 Table A Studno Name cs1 Kannan cs3 Lenin cs4 Padmaja
 Table B Studno Name cs1 Kannan cs2 GowriShankarn cs3 Lenin

Result

 Table A ∪ B Studno . cs1 Kannan cs2 GowriShankarn cs3 Lenin cs4 Padmaja

SET DIFFERENCE ( Symbol: -)
The result of A – B, is a relation that includes all tuples that are in A but not in B. The attribute name of A has to match with the attribute name in B.

Example 4:
( using Table B)
Result

 Table A - B cs4 Padmaja

INTERSECTION (symbol: ∩) A∩B
Defines a relation consisting of a set of all tuples that is in both in A and B. However, A and B must be union-compatible

Example 5:
(using Table B)

 A ∩ B cs1 Kannan cs3 Lenin

PRODUCT OR CARTESIAN PRODUCT (Symbol: X)

Cross product is a way of combining two relations. The resulting relation contains, both relations being combined.
A × B means A times B, where the relation A and B have different attributes.
This type of operation is helpful to merge columns from two relations.

Cartesian Product

 Table A Table B studno name studno subject cs1 Kannan cs28 Big Data cs2 Gowri Shankar cs62 R language cs4 Padmaja cs25 python programming

Cartesian product : Table A × Table B

 studno name course subject cs1 Kannan cs28 Big Data cs1 Kannan cs62 R language cs1 Kannan cs25 python programming cs2 Gowri Shankar cs28 Big Data cs2 Gowri Shankar cs62 R language cs2 Gowri Shankar cs25 python programming cs4 Padmaja cs28 Big Data cs4 Padmaja cs62 R language cs4 Padmaja cs25 python programming
Concept: Relational Algebra in DBMS
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