In eduladder you can Ask,Answer,Listen,Earn and Download Questions and Question papers.

Watch related videos of your favorite subject.

Connect with students from different parts of the world.

Apply or Post Jobs, Courses ,Internships and Volunteering opportunity. For FREE

See Our team

Wondering how we keep quality?

Got unsolved questions? Ask Questions

GATE
GMAT
CBSE
NCERT
Career
Interview
Railway
UPSC
NID
NIFT-UG
NIFT-PG
PHP
AJAX
JavaScript
Node Js
Shell Script
Research

## What are the fundamental operations of relational algebra. Define each. - Database management system

## Presidency University, Bangalore- Database management system questions

Asked On2017-07-06 05:51:46 by:Aparna-Dasgupta

Taged users:

Likes:

Be first to like this question

Dislikes:

Be first to dislike this question

Talk about this Like Dislike

Download question setAnswersRelational database systems are expected to be equipped with a query language that can assist its users to query the database instances. There are two kinds of query languages − relational algebra and relational calculus.

Relational Algebra

Relational algebra is a procedural query language, which takes instances of relations as input and yields instances of relations as output. It uses operators to perform queries. An operator can be either unary or binary. They accept relations as their input and yield relations as their output. Relational algebra is performed recursively on a relation and intermediate results are also considered relations.

Select Operation (σ)

It selects tuples that satisfy the given predicate from a relation.

Notation − σp(r)

Where σ stands for selection predicate and r stands for relation. p is prepositional logic formula which may use connectors like and, or, and not. These terms may use relational operators like − =, ≠, ≥, < , >, ≤.

For example −

σsubject = "database"(Books)

Output − Selects tuples from books where subject is 'database'.

σsubject = "database" and price = "450"(Books)

Output − Selects tuples from books where subject is 'database' and 'price' is 450.

σsubject = "database" and price = "450" or year > "2010"(Books)

Output − Selects tuples from books where subject is 'database' and 'price' is 450 or those books published after 2010.

Project Operation (∏)

It projects column(s) that satisfy a given predicate.

Notation − ∏A1, A2, An (r)

Where A1, A2 , An are attribute names of relation r.

Duplicate rows are automatically eliminated, as relation is a set.

For example −

∏subject, author (Books)

Selects and projects columns named as subject and author from the relation Books.

Union Operation (∪)

It performs binary union between two given relations and is defined as −

r ∪ s = { t | t ∈ r or t ∈ s}

Notation − r U s

Where r and s are either database relations or relation result set (temporary relation).

For a union operation to be valid, the following conditions must hold −

r, and s must have the same number of attributes.

Attribute domains must be compatible.

Duplicate tuples are automatically eliminated.

∏ author (Books) ∪ ∏ author (Articles)

Output − Projects the names of the authors who have either written a book or an article or both.

Set Difference (−)

The result of set difference operation is tuples, which are present in one relation but are not in the second relation.

Notation − r − s

Finds all the tuples that are present in r but not in s.

∏ author (Books) − ∏ author (Articles)

Output − Provides the name of authors who have written books but not articles.

Cartesian Product (Χ)

Combines information of two different relations into one.

Notation − r Χ s

Where r and s are relations and their output will be defined as −

r Χ s = { q t | q ∈ r and t ∈ s}

σauthor = 'tutorialspoint'(Books Χ Articles)

Output − Yields a relation, which shows all the books and articles written by tutorialspoint.

Rename Operation (ρ)

The results of relational algebra are also relations but without any name. The rename operation allows us to rename the output relation. 'rename' operation is denoted with small Greek letter rho ρ.

Notation − ρ x (E)

Where the result of expression E is saved with name of x.

Additional operations are −

Set intersection

Assignment

Natural join

Relational Calculus

In contrast to Relational Algebra, Relational Calculus is a non-procedural query language, that is, it tells what to do but never explains how to do it.

Relational calculus exists in two forms −

Tuple Relational Calculus (TRC)

Filtering variable ranges over tuples

Notation − {T | Condition}

Returns all tuples T that satisfies a condition.

For example −

{ T.name | Author(T) AND T.article = 'database' }

Output − Returns tuples with 'name' from Author who has written article on 'database'.

TRC can be quantified. We can use Existential (∃) and Universal Quantifiers (∀).

For example −

{ R| ∃T ∈ Authors(T.article='database' AND R.name=T.name)}

Output − The above query will yield the same result as the previous one.

Domain Relational Calculus (DRC)

In DRC, the filtering variable uses the domain of attributes instead of entire tuple values (as done in TRC, mentioned above).

Notation −

{ a1, a2, a3, ..., an | P (a1, a2, a3, ... ,an)}

Where a1, a2 are attributes and P stands for formulae built by inner attributes.

For example −

{< article, page, subject > | ∈ TutorialsPoint ∧ subject = 'database'}

Output − Yields Article, Page, and Subject from the relation TutorialsPoint, where subject is database.

Just like TRC, DRC can also be written using existential and universal quantifiers. DRC also involves relational operators.

The expression power of Tuple Relation Calculus and Domain Relation Calculus is equivalent to Relational Algebra.

Likes:

Be first to like this answer

Dislikes:

Be first to dislike this answer

Talk about this Like Dislike

Lets together make the web is a better placeWe made eduladder by keeping the ideology of building a supermarket of all the educational material available under one roof. We are doing it with the help of individual contributors like you, interns and employees. So the resources you are looking for can be easily available and accessible also with the freedom of remix reuse and reshare our content under the terms of creative commons license with attribution required close.

You can also contribute to our vision of "Helping student to pass any exams"with these.Answer a question:You can answer the questions not yet answered in eduladder.How to answer a questionCareer:Work or do your internship with us.Work with usCreate a video:You can teach anything and everything each video should be less than five minutes should cover the idea less than five min.How to upload a video on eduladder