1.Sets and Their Representation Class 11:

Sets and Their Representation Class 11

The concept of Sets and Their Representation Class 11 serves as a fundamental parts of the present day mathematics.Today this concept is being used in almost every branch of mathematics.Sets are used to define the concepts of relations and functions.We will study about above the article.

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2.Important Facts of Sets and Their Representation Class 11:-

Sets and Their Representation Class 11

(1.)Set used particularly in Mathematics viz
N:the set of all natural numbers
Z:the set of all integers
Q:the set of all rational numbers
R:the set of real numbers
Z^{+} :the set of positive integers
Q^{+} :the set of positive rational numbers, and
R^{+} :the set of positive real numbers
(2.)(i).Obiects,elements and members of a set are synonymous terms
(ii)Sets are usually denoted by capital letters A,B,C,X,Y,Z, etc.
(iii)The elements of a set are represented by small letters a,b,c,x,y,z,etc.
(3.)Method of Representing a Set
(i).Roster or tabular form
In roster form,all the elements of a set are listed,the elements are being separated by commas and are enclosed with braces {}. (curly bracket) for example,if the set of all odd natural numbers less than 10 is represented by A,then A={1,3,5,7,9}
(ii).Set-builder form or rule form
In set-builder form,all the elements of a set possess a single common property which is not possessed by any elements outside the set.For example,in elements possess a common property, namely,each of them is a vowel in English albhabet, and no other letter possess this property.Denoting this set by V,we write
V={x:x is a vowel in English albhabet}
Set are Represented in Both form in following Table

3.Sets and Their Representation Class 11 Illustrations:-

Illustration:1.Which of the following are sets? Justify your answer.
(i).The collection of all the months of a year beginning with the letter J.
Solution:{January,June,July}
It is a set, because one can definitively identify the months starting with the letter ‘J’.
(ii).The collection of ten most talented writers of India.
Solution:It is not a set,because the criteria for determining the most talented writers can vary from person to person.
(iii).A team of eleven best-cricket batsmen of the world.
Solution:It is not a set,because the criteria for identifying the best batsmen in the world can vary from person to person.
(iv).The collection of all boys in your class.
Solution:It is a set,because the collection of students in a particular class is well-defined.
(v). The collection of all natural numbers less than 100.
Solution:{1,2,3,4,5,……., 99}
It is a set,because the natural numbers less than 100 are well-defined.
(vi). A collection of novels written by the writer Munshi Prem Chand.
Solution:It is a set,because the collection of novels written by the author Premchand is well-defined.
(vii).The collection of all even integers.
Solution: \{\ldots,-4,-2,0,2,4,\ldots\}
It is a set, because the collection of even integers is well-defined.
(viii).The collection of questions,in this Chapter.
Solution:It is a set,because all the questions in this chapter are well-defined.
(6) A collection of most dangerous animals of the world.
Solution:It is not a set,because the criteria for identifying the most dangerous animals in the world can vary from person to person.
Illustration:2. Let A={1,2,3,4,5,6} insert the appropriate symbole \in or \notin in the blank spaces-
(i).5……A
Solution: 5 \in A
(ii).8……A
Solution: 8 \notin A
(iii).0……A
Solution: 0 \notin A
(iv).4……A
Solution: 4 \in A
(v).2……A
Solution: 2 \in A
(vi).10……A
Solution: 10 \notin A

Sets and Their Representation Class 11

Illustration:3.Write the following sets in roster form.
(i).A ={x:x is an integer and -3 \leq x <7 }
Solution:{-3,-2,-1,0,1,2,3,4,5,6}
(ii).B={x:x is a natural number less than 6}
Solution:B={1,2,3,4,5}
(iii).C={x:x is a two-digit natural number such that the sum of its digits is 8}
Solution: C={17,26,35,44,62,71,80}
(iv).D ={x:x is a prime number which is divisor of 60}
Solution:D={2,3,5}
(v).E=The set of all letters in the word TRIGONOMETRY
Solution:{T,R,I,G,O,N,M,E,Y}
(vi).F=The set of all letters in the word BETTER
Solution:{B,E,T,R}
Illustration:4.Write the following sets in the set-builder form:
Illustration:4(i).{3,6,9,12}
Solution: \{x: x=3n, n\in N, \text{and } 1 \leq n \leq 4\}
Illustration:4(ii).{2,4,8,16,32}
Solution: \{x:x=2^n,\;n\in\mathbb N, \text{and } 1 \leq n \leq 5\}
Illustration:4(iii).{5,25,125,625,}
Solution: \{x:x=5^n,\;n\in\mathbb N,\text{and } 1 \leq n \leq 4\}
Illustration:4(iv).{2,4,6}
Solution: \{x:x=2n,\;n\in\mathbb N, \text{and } 1 \leq n \leq 3\}
Illustration:4(v).{1,4,9,……,100}
Solution: \{x:x=n^2,\;n\in\mathbb N, \text{and } 1 \leq n \leq 10\}
Illustration:5.List all the elements of the following :
(i).A ={x:x is an odd natural number)
Solution:A={1,3,5,7,…….}
(ii).B={x:x is an intger -\frac{1}{2} <x < \frac{9}{2} }
Solution:B={0,1,2,3,4}
(iii).C={x:x is an integer, x^2 \leq 4 }
Solution:C={-2,-1,0,1,2}
(iv)D={x:x a letter in the word “LOYAL”}
Solution:D={L,O,Y,A}
(v) E={x:x is a month of a year not having 31 days}
Solution:E={February,April,June,September,November}
(vi) F={x:x is a consonant in the English alphabet which precedes k}.
Solution:F={b,c,d,f,g,h}
Illustration:6.Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

Solution:

With the above illustrations,one can understand the Sets and Their Representation Class 11.

Also Read This Article:- Set theory

4.Sets and Their Representation Class 11 Practice Questions for Students:

Sets and Their Representation Class 11

(1.)Write the set A={x:x is a positive integer and x^2<4 } in the roster form.
(2.)Write the set in the set A=\left\{\frac12,\frac23,\frac34,\frac45,\frac56\right\} builder form.
Answers:(1.)A={1,2,3,4,5,6}
(2.) A=\left\{x :x=\frac{n}{n+1}:n \in\mathbb{N}, 1 \leq n \leq 5\right\}
By solving the above questions,you can understand the Sets and Their Representation Class 11 well because the concept is well understood when you solve it practically.

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5.Frequently Asked Questions Related to Sets and Their Representation Class 11:

This article has been prepared by **Satyam Coaching Centre** on the **Satyam Mathematics** blog.”*
\begin{array}{|c|} \hline \text{छात्र-छात्राओं से आज का सवाल } \\ \text{वह कौन-सी संख्या है,जिसमें 7 से भाग} \\ \text{ देने पर या उसमें 7 घटाने पर समान उत्तर प्राप्त होता है।} \\ \text{दिनांक 23.06.2026 के प्रश्न का उत्तर:28 स्तम्भ } \\ (8+8+6+6=28) \\ \text{Today's Question to Students } \\ \text{What is the number in which dividing by 7 } \\ \text{or subtracting it by 7 gives the same answer? } \\ \text{Answer to Question Dated 23.06.2026:28 Pillar } \\ (8+8+6+6=28) \\ \hline \end{array}