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Short Intro

In this post, students can find complete step-by-step solutions for Class 11 Maths Chapter 1 Exercise 2.1 – Sets based on the latest NCERT syllabus. This exercise covers basic concepts of sets, roster form, set-builder form, empty sets, finite and infinite sets, subsets, intervals, union, intersection and difference of sets in an easy and exam-oriented format.

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Quick Information Box

Item	Details
Board	NCERT / CBSE
Class	11
Subject	Mathematics
Chapter	Sets
Exercise	1.1
Main Topics	Sets & Operations

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Concepts Used (Topics Covered)

• Definition of Sets
• Roster Form
• Set-Builder Form
• Empty Set
• Finite & Infinite Sets
• Equal Sets
• Subsets
• Universal Set
• Union of Sets
• Intersection of Sets
• Difference of Sets
• Venn Diagrams

The chapter introduces the fundamental concept of sets and their applications in mathematics.

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Important Formulas

Union of Sets

$A\cup B=\{x:x\in A\text{ or }x\in B\}$

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Intersection of Sets

$A\cap B=\{x:x\in A\text{ and }x\in B\}$

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Difference of Sets

$A-B=\{x:x\in A\text{ and }x\notin B\}$

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Complement of Set

$A’=U-A$

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Questions & Step-by-step Solutions

Question 1

Which of the following are sets?

Solution

(i) Collection of months beginning with J

Set

because it is well-defined.

(ii) Collection of ten most talented writers

Not a set

because “talented” is not well-defined.

(iii) Eleven best cricket batsmen

Not a set

(iv) All boys in your class

Set

(v) Natural numbers less than 100

Set

(vi) Novels written by Munshi Prem Chand

Set

(vii) Collection of all even integers

Set

(viii) Collection of questions in this chapter

Set

(ix) Collection of most dangerous animals

Not a set

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Question 2

Let:

A = {1,2,3,4,5,6}

Insert ∈ or ∉.

Solution

(i)

5 ∈ A

(ii)

8 ∉ A

(iii)

0 ∉ A

(iv)

4 ∈ A

(v)

2 ∈ A

(vi)

10 ∉ A

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Question 3

Write the following in roster form.

(i)

$A=\{x:-3\le x<7,x\in Z\}$

Solution

A = {−3,−2,−1,0,1,2,3,4,5,6}

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(ii)

$B=\{x:x\text{ is natural number less than }6\}$

Solution

B = {1,2,3,4,5}

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(iii)

Two-digit natural numbers whose digits sum to 8.

Solution

C = {17,26,35,44,53,62,71,80}

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(iv)

Prime divisors of 60.

Solution

D = {2,3,5}

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(v)

Letters in TRIGONOMETRY

Solution

E = {T,R,I,G,O,N,M,E,Y}

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(vi)

Letters in BETTER

Solution

F = {B,E,T,R}

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Question 4

Write in set-builder form.

(i)

{3,6,9,12}

Solution

$A=\{x:x=3n,n\in N,1\le n\le4\}$

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(ii)

{2,4,8,16,32}

Solution

$B=\{x:x=2^n,n=1,2,3,4,5\}$

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(iii)

{5,25,125,625}

Solution

$C=\{x:x=5^n,n=1,2,3,4\}$

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Question 5

List all elements.

(i)

Odd natural numbers

Solution

A = {1,3,5,7,9,...}

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(ii)

Integers satisfying:

$-\frac12<x<\frac92$

Solution

B = {0,1,2,3,4}

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(iii)

Integers satisfying:

$x^2\le4$

Solution

C = {−2,−1,0,1,2}

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(iv)

Letters in LOYAL

Solution

D = {L,O,Y,A}

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(v)

Months not having 31 days

Solution

E = {February, April, June, September, November}

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Question 6

Match the sets.

Solution

(i)

{1,2,3,6} → divisors of 6

(ii)

{2,3} → prime divisors of 6

(iii)

{M,A,T,H,E,I,C,S} → letters of MATHEMATICS

(iv)

{1,3,5,7,9} → odd natural numbers less than 10

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Common Mistakes

• Repeating elements in roster form
• Confusing ∈ and ⊂
• Writing incorrect set-builder notation
• Ignoring distinct elements
• Using undefined collections as sets

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Exam Tips

• Learn proper symbols carefully.
• Practice roster and set-builder conversion.
• Memorize standard set notations.
• Draw Venn diagrams for clarity.

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Practice MCQs

MCQ 1

Which is a well-defined collection?

A. Beautiful flowers
B. Best students
C. Prime numbers less than 20
D. Intelligent boys

Answer:

C. Prime numbers less than 20

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MCQ 2

Which symbol denotes “belongs to”?

A. ⊂
B. ∈
C. ∪
D. ∩

Answer:

B. ∈

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MCQ 3

Set of vowels is:

{a,e,i,o,u}

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FAQ Section

What is a set?

A well-defined collection of objects is called a set.

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What is roster form?

Listing all elements inside braces.

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What is an empty set?

A set having no element.

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What is subset?

If every element of A belongs to B, then A is subset of B.

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