Access free live classes and tests on the app
Download
+
Unacademy
  • Goals
    • AFCAT
    • AP EAMCET
    • Bank Exam
    • BPSC
    • CA Foundation
    • CAPF
    • CAT
    • CBSE Class 11
    • CBSE Class 12
    • CDS
    • CLAT
    • CSIR UGC
    • GATE
    • IIT JAM
    • JEE
    • Karnataka CET
    • Karnataka PSC
    • Kerala PSC
    • MHT CET
    • MPPSC
    • NDA
    • NEET PG
    • NEET UG
    • NTA UGC
    • Railway Exam
    • SSC
    • TS EAMCET
    • UPSC
    • WBPSC
Login Join for Free
avtar
  • ProfileProfile
  • Settings Settings
  • Refer your friendsRefer your friends
  • Sign outSign out
  • Terms & conditions
  • •
  • Privacy policy
  • About
  • •
  • Careers
  • •
  • Blog

© 2023 Sorting Hat Technologies Pvt Ltd

  • CAT 2023
  • Study Materials
  • Notifications
  • CAT Syllabus
  • CAT Mock Test
  • CAT Exam Pattern
  • CAT Question Paper
  • CAT Preparation Books
  • Downloads
  • Important Formulas
  • Eligibility Criteria
CAT 2023 » CAT Study Material » Data Interpretation and Logical Reasoning » Representation of Sets
scholarship_cat

Representation of Sets

Sets are defined as a collection of well-defined items or elements that do not vary from one person to the next. Read the content to know more.

Table of Content
  •  

An unsorted collection of items known as elements or set members is referred to as a set.

‘a ∉ A’ denotes the absence of an element ‘a’ from the set A.

Types of Set Representation

A set can be represented in a number of ways. 

  1. Statement form.
  2. Using a roster or a tabular form

3: Set Builder

1. Statement Form

In this form, the elements of the set are specified in depth. Listed below are some examples.

  1. A group of all even numbers less than 10.
  2. The number is in the range of ten to one.

2. Roster form

In this diagram, the elements are given in brackets with commas separating them. Below are two examples of this.

  1. Assume that N is a collection of natural numbers less than 5.

N = { 1 , 2 , 3, 4 }.

  1. The alphabet’s vowels.

V = { a , e , I , o , u }.

3. Set builder form

A property must be fulfilled by each member of a Set-builder set.

  1. x: x is a divisible by six even number less than 100.
  2. x is a number less than ten.

If and only if every element of set A is also a part of set B, that set is said to be a subset of another set B.

‘A ⊆ B’ denotes that A is a subset of B.

Elements

A set can contain components like numbers, states, vehicles, people, and even other sets. Anything can be used to construct a set, but there are a few things to keep in mind.

Pairs of equals

Elements of a set can be in or out. A set could be described using a defining attribute or a list of its elements. It doesn’t matter if they’re listed in any particular sequence. The sets {1, 2, 3} and {1, 3, 2} are equivalent since they both contain the same items.

Two unique sets

There are two sets that stand out in particular. The first is the universal set, also known as U. All of the potential elements are included in this set. This set could vary from one setup to the next. One universal set might be the set of real numbers, whereas another might be the whole numbers 0 to 2, and so on.

The other group that requires attention is the empty set. The empty set is a collection of zero elements. This can be written as and is symbolised by the symbol.

Set Operations

Setup Procedures There are various procedures, however they virtually all consist of the three described below:

The combining of two or more persons is referred to as a union. The union of the sets A and B consists of objects that belong to either A or B.

A crossroads is a point where two things meet. The intersection of the two sets consists of items that appear in both A and B. The complement of A is made up of all components in the universal set that are not constituents of A.

Venn diagrams are a form of diagram used to show relationships between objects.

A Venn diagram is a visual representation of the relationship between two sets of information. For our case, a rectangle represents the universal set. Each group has a circle as its symbol. The circles overlapping indicate the intersection of our two sets.

Set Theory in Application

Set theory is used frequently in mathematics. It is the cornerstone of several mathematical subfields. Probability and statistical sciences are where it is most widely used. Many probability ideas are based on the implications of set theory. One way to express probability principles is through set theory.

Conclusion 

Sets can be represented in two ways: the Roster form and the Set-Builder form. Both of these forms can be used to describe the same data, but the style differs in each case. A collection of well-specified data is defined as a set. In mathematics, a set is a tool that may be used to classify and collect data from the same category, even though the items in the set are entirely different from one another.

Sets are an important idea in modern mathematics. Sets are now employed in practically every discipline of mathematics in the modern period. A set is a group of specific objects or a collection of specific things in mathematics. Relationships and functions are defined in terms of sets. A strong understanding of sets is necessary for the study of probability, geometry, and other subjects. The sets can take a variety of formats. The fundamentals of set theory and set representation will be covered in depth in this essay.

faq

Frequently asked questions

Get answers to the most common queries related to the CAT Examination Preparation.

What are the three different ways to represent a collection of items?

A set is a group of objects that are all different. Elements or members of the set are two terms that can be used to...Read full

What is the best way to depict a set's element?

The symbol is used to indicate that a specific item is part of a set. The sign indicates that an item isn’t pa...Read full

In memory, how are sets stored?

Set Representation is a term that refers to the representation of a collection of ...Read full

In mathematics, why are sets significant?

Sets are used to hold a group of objects that are all connected. They are crucial in mathematics since sets are used...Read full

What is the depiction of a set-builder?

Set-builder notation is a way of writing and representing the elements of sets, especially ones with an infinite num...Read full

A set is a group of objects that are all different. Elements or members of the set are two terms that can be used to describe the things. Because an element is either a member of the set or it isn’t, a set does not list the same element twice.

A set can be identified in one of three ways:

a description in words,

List or Roster method

Set builder Notation

The symbol is used to indicate that a specific item is part of a set. The sign indicates that an item isn’t part of a set. The cardinal number, or cardinality, of a set is the number of components.

Set Representation is a term that refers to the representation of a collection of Sets can be represented in two ways: the Roster form and the Set-Builder form. Both of these forms can be used to describe the same data, but the style differs in each case.

Sets are used to hold a group of objects that are all connected. They are crucial in mathematics since sets are used or referred to in almost every subject. They are necessary for the construction of more complicated mathematical structures.

Set-builder notation is a way of writing and representing the elements of sets, especially ones with an infinite number of them. Integers, real numbers, and natural numbers are examples of numbers that are commonly utilised.

Crack CAT with Unacademy

Get subscription and access unlimited live and recorded courses from India’s best educators

  • Structured syllabus
  • Daily live classes
  • Ask doubts
  • Tests & practice
Learn more

Notifications

Get all the important information related to the CAT Exam including the process of application, important calendar dates, eligibility criteria, exam centers etc.

CAT Eligibility Criteria 2023
CAT Exam Pattern 2023
CAT Result 2022
CAT Syllabus 2023 – CAT Exam Syllabus – Download PDF
GMAT Exam Notification
IBSAT 2022 Notification
IIFT Notification
MAH CET Notification
MICAT Notification
NMAT Notification
SNAP Notification
TISSNET Notification
Top Colleges in India That Accept CAT Score
XAT Notification
See all

Related articles

Learn more topics related to Data Interpretation and Logical Reasoning
Wilson Remainder Theorem

To reduce huge numbers with regard to a certain modulus and to solve congruences, Wilson's theorem and Fermat's theorem can be employed.

Why Use the Critical Path Method

A brief note on Why use the critical path method, Improves future planning, Facilitates more effective resource management, Helps avoid bottlenecks and many things.

What is Types of Analogy Reasoning

In this lecture we’re going to learn about types of analogy reasoning, the number based/numerical analogy, letter and number based analogy and general knowledge-based analogy, questions based on analogy and many more things.

What is Posterior Probability

A posterior probability, in Bayesian records, is the revised or updated probability of an event happening after taking into account new records. The posterior probability is calculated by updating the prior probability by using Bayes’ theorem. In statistical phrases, the posterior probability is the probability of event A taking place given that event B has taken place.

See all
Access more than

469+ courses for CAT – Optional

Get subscription

Trending Topics

  • CAT Mock Test
  • CAT Question Papers
  • CAT 2021 Question Paper
  • CAT 2020 Question Paper
  • CAT Question Paper 2019 PDF
  • Best Books for CAT Preparation
  • CAT Eligibility Criteria
  • CAT Syllabus
  • CAT Exam Pattern
  • CAT Result
combat_cat

Related links

  • Co-ordinate Geometry applications
  • What Is A Polygon?
  • Uses of a Quadrilateral
  • Algebraic Identities
  • SPSS Full Form
  • Geometric Progression’s Uses
  • Blood Relation Questions
freeliveclasses_cat
CAT 2021 Question Paper
.

Latest Notifications

  • CAT Exam Dates(Out) – Check how to register
  • CAT 2022 Registration (3rd Aug) – How to apply, Last Date & Fees
  • CAT 2022 Exam Notification
Company Logo

Unacademy is India’s largest online learning platform. Download our apps to start learning


Starting your preparation?

Call us and we will answer all your questions about learning on Unacademy

Call +91 8585858585

Company
About usShikshodayaCareers
we're hiring
BlogsPrivacy PolicyTerms and Conditions
Help & support
User GuidelinesSite MapRefund PolicyTakedown PolicyGrievance Redressal
Products
Learner appLearner appEducator appEducator appParent appParent app
Popular goals
IIT JEEUPSCSSCCSIR UGC NETNEET UG
Trending exams
GATECATCANTA UGC NETBank Exams
Study material
UPSC Study MaterialNEET UG Study MaterialCA Foundation Study MaterialJEE Study MaterialSSC Study Material

© 2023 Sorting Hat Technologies Pvt Ltd

Unacademy
  • Goals
    • AFCAT
    • AP EAMCET
    • Bank Exam
    • BPSC
    • CA Foundation
    • CAPF
    • CAT
    • CBSE Class 11
    • CBSE Class 12
    • CDS
    • CLAT
    • CSIR UGC
    • GATE
    • IIT JAM
    • JEE
    • Karnataka CET
    • Karnataka PSC
    • Kerala PSC
    • MHT CET
    • MPPSC
    • NDA
    • NEET PG
    • NEET UG
    • NTA UGC
    • Railway Exam
    • SSC
    • TS EAMCET
    • UPSC
    • WBPSC

Share via

COPY