Question

Explain the different operators in Relational algebra with suitable examples.

Answer 1

Relational Algebra Operations from Set Theory

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

SELECT (symbol: σ)

General form σ_c ( 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_course (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