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NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1

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NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.1 - FREE PDF Download

NCERT Solutions for Class 11 Maths Chapter 1 - Sets Exercise 1.1 explains the foundation of modern mathematics! Class 11th Maths 1 Exercise 1.1 answers introduce students to sets, a fundamental idea that underpins much of mathematics. This Exercise is student's first step into this exciting topic, where students will learn about sets' basics and essential properties.

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Through this Ex 1.1 Class 11, students will develop a solid grasp of the basic concepts, which will serve as a building block for more advanced topics in mathematics.

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Access NCERT Solutions for Maths Class 11 Chapter 1 Sets Exercise 1.1

Exercise (1.1)

1. Which of the following are sets? Justify your answer.

i. The collection of all months of a year beginning with the letter J.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

We can definitely identify the collection of months beginning with a letter J.

Thus, the collection of all months of a year beginning with the letter J is the set.


ii. The collection of ten most talented writers of India

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

The criteria for identifying the collection of ten most talented writers of India may vary from person to person. So it is not a well-defined object.

Thus, the collection of ten most talented writers of India is not a set.


iii. A team of eleven best cricket batsmen of the world.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

The criteria for determining the eleven best cricket batsmen may vary from person to person. So it is not a well-defined object.

Thus, a team of eleven best cricket batsmen in the world is not a set.


iv. The collection of all boys in your class.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

We can definitely identify the boys who are all studying in the class. So it is a well-defined object.

Thus, the collection of all boys in your class is a set.


v. The collection of all natural numbers less than $100$.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

We can identify the natural numbers less than $100$ can easily be identified. So it is a well-defined object.

Thus, the collection of all natural numbers less than $100$ is a set.


vi. A collection of novels written by the writer Munshi Prem Chand.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

We can identify the books that belong to the writer Munshi Prem Chand. So it is a well-defined object.

Thus, a collection of novels written by the writer Munshi Prem Chand is a set.


vii. The collection of all even integers.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

We can identify integers that are all the collection of even integers. So it is not a well-defined object.

Thus, the collection of all even integers is a set.


viii. The collection of questions in this chapter.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

We can easily identify the questions that are in this chapter. So it is a well-defined object.

Thus, the collection of questions in this chapter is a set.


ix. A collection of the most dangerous animals in the world.

Ans:

To determine if the given statement is a set

A set is a collection of well-defined objects.

The criteria for determining the most dangerous animals may vary according to the person. So it is not a well-defined object.

Thus, the collection of the most dangerous animals in the world is a set.


2. Let $A=\left\{ 1,2,3,4,5,6 \right\}$. Insert the appropriate symbol $\in $ or $\notin $ in the blank spaces:

i. $5...A$

Ans:

Given that,

$A=\left\{ 1,2,3,4,5,6, \right\}$

To insert the appropriate symbol $\in $ or $\notin $

The number $5$ is in the set.

$\therefore 5\in A$


ii. $8...A$

Ans:

Given that,

$A=\left\{ 1,2,3,4,5,6, \right\}$

To insert the appropriate symbol $\in $ or $\notin $

The number $8$ is not in the set.

$\therefore 8\notin A$


iii. $0...A$

Ans:

Given that,

$A=\left\{ 1,2,3,4,5,6, \right\}$

To insert the appropriate symbol $\in $ or $\notin $

The number $0$ is not in the set.

$\therefore 0\notin A$


iv. $4...A$

Ans:

Given that,

$A=\left\{ 1,2,3,4,5,6, \right\}$

To insert the appropriate symbol $\in $ or $\notin $

The number $4$ is in the set.

$\therefore 4\in A$


v. $2...A$

Ans:

Given that,

$A=\left\{ 1,2,3,4,5,6, \right\}$

To insert the appropriate symbol $\in $ or $\notin $

The number $2$ is in the set.

$\therefore 2\in A$


vi. $10...A$

Ans:

Given that,

$A=\left\{ 1,2,3,4,5,6, \right\}$

To insert the appropriate symbol $\in $ or $\notin $

The number $10$ is not in the set.

$\therefore 10\notin A$


3. Write the following sets in roster form:

i. $A=\left\{ x:x\text{ is an integer and -3x7} \right\}$

Ans:

Given that,

$A=\left\{ x:x\text{ is an integer and -3x7} \right\}$

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The elements of the set are $-2,-1,0,1,2,3,4,5,6$.

$\therefore $ The roaster form of the set $A=\left\{ x:x\text{ is an integer and -3x7} \right\}$ is $A=\left\{ -2,-1,0,1,2,3,4,5,6 \right\}$.


ii. $B=\left\{ x:x\text{ is a natural number less than 6} \right\}$

Ans:

Given that,

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

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The elements of the set are $1,2,3,4,5$.

$\therefore$ The roaster form of the set $B=\left\{ x:x\text{ is a natural number less than 6} \right\}$ is $B=\left\{ 1,2,3,4,5 \right\}$.


iii. $C=\left\{ x:x\text{ is a two-digit natural number such that sum of its digits is 8} \right\}$

Ans:

Given that,

$C=\left\{ x:x\text{ is a two-digit natural number such that sum of its digits is 8} \right\}$

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The elements of the set are $17,26,35,44,53,62,71,80$ such that their sum is 8

∴ The roaster form of the set $C={x:x \;{\text {is a two-digit natural number such that the sum of its digits is 8}}}$ is $\left\{ 17,26,35,44,53,62,71,80 \right\}$.


iv. $D=\left\{ x:x\text{ is a prime number which is divisor of 60} \right\}$

Ans:

Given that,

$D=\left\{ x:x\text{ is a prime number which is divisor of 60} \right\}$

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The divisors of $60$ are $2,3,4,5,6$. Among these the prime numbers are $2,3,5$

The elements of the set are $2,3,5$.

$\therefore $ The roaster form of the set $D=\left\{ x:x\text{ is a prime number which is divisor of 60} \right\}$ is $D=\left\{ 2,3,5 \right\}$.


v. $E=$The set of all letters in the word TRIGONOMETRY

Ans:

Given that,

$E=$The set of all letters in the word TRIGONOMETRY

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

There are $12$ letters in the word TRIGONOMETRY out of which T, R and O gets repeated.

The elements of the set are T, R, I G, O, N, M, E, Y.

$\therefore $ The roaster form of the set $E=$The set of all letters in the word TRIGONOMETRY is $E=\left\{ T,R,I,G,O,N,M,E,Y \right\}$.


vi. $F=$The set of all letters in the word BETTER

Ans:

Given that,

$F=$The set of all letters in the word BTTER

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

There are $6$ letters in the word BETTER out of which E and T are repeated.

The elements of the set are B, E, T, R.

$\therefore $ The roaster form of the set $F=$The set of all letters in the word BTTER

 is $F=\left\{ B,E,T,R \right\}$.


4. Write the following sets in the set builder form:

i. $\left( 3,6,9,12 \right)$

Ans:

Given that,

$\left\{ 3,6,9,12 \right\}$

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set are multiple of $3$ from $1$ to $4$ such that $\left\{ x:x=3n,n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$

$\therefore \left\{ 3,6,9,12 \right\}=\left\{ x:x=3n,n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$


ii. $\left\{ 2,4,8,16,32 \right\}$

Ans:

Given that,

{2,4,8,16,32}

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set are powers of $2$ from $1$ to $5$ such that $\left\{ x:x={{2}^{n}},n\in N\text{ and 1}\le \text{n}\le 5 \right\}$

$\therefore \left\{ 2,4,8,16,32 \right\}=\left\{ x:x={{2}^{n}},n\in N\text{ and 1}\le \text{n}\le 5 \right\}$


iii. $\left\{ 5,25,125,625 \right\}$

Ans:

Given that,

$\left\{ 5,25,125,625 \right\}$

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set are powers of $5$ from $1$ to $4$ such that $\left\{ x:x={{5}^{n}},n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$

$\therefore \left\{ 5,25,125,625 \right\}=\left\{ x:x={{5}^{n}},n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$


iv. $\left\{ 2,4,6,... \right\}$

Ans:

Given that,

$\left\{ 2,4,6,... \right\}$

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers are the set of all even natural numbers.

$\therefore \left\{ 2,4,6,... \right\}=\left\{ x:x\text{ is an even natural number} \right\}$


v. $\left\{ 1,4,9,...100 \right\}$

Ans:

Given that,

$\left\{ 1,4,9,...100 \right\}$

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set squares of numbers form $1$ to $10$ such that $\left\{ x:x={{n}^{2}},n\in N\text{ and 1}\le \text{n}\le 10 \right\}$

$\therefore \left\{ 1,4,9,...100 \right\}=\left\{ x:x={{n}^{2}},n\in N\text{ and 1}\le \text{n}\le 10 \right\}$


5. List all the elements of the following sets:

i. $A=\left\{ x:x\text{ is an odd natural number} \right\}$

Ans:

Given that,

$A=\left\{ x:x\text{ is an odd natural number} \right\}$

To list the elements of the given set

The odd natural numbers are $1,3,5,...$

$\therefore $ The set $A=\left\{ x:x\text{ is an odd natural number} \right\}$ has the odd natural numbers that are $\left\{ 1,3,5,... \right\}$


ii. $B=\left\{ x:x\text{ is an integer;-}\frac{1}{2}<x<\frac{9}{2} \right\}$

Ans:

Given that,

$B=\left\{ x:x\text{ is an integer;-}\frac{1}{2}<x<\frac{1}{2} \right\}$

To list the elements of the given set

$-\frac{1}{2}=-0.5$ and $\frac{9}{2}=4.5$

So the integers between $-0.5$ and $4.5$ are $0,1,2,3,4$

$\therefore $ The set $B=\left\{ x:x\text{ is an integer;-}\frac{1}{2}<x<\frac{1}{2} \right\}$ has an integers that are between $\left\{ 0,1,2,3,4 \right\}$


iii. $C=\left\{ x:x\text{ is an integer;}{{\text{x}}^{2}}\le 4 \right\}$

Ans:

Ans:

Given that,

$C=\left\{ x:x\text{ is an integer;}{{\text{x}}^{2}}\le 4 \right\}$

To list the elements of the given set

It is observed that,

${{x}^{2}}\le 4$

${{\left( -2 \right)}^{2}}=4\le 4$

${{\left( -1 \right)}^{2}}=1\le 4$

${{\left( 0 \right)}^{2}}=0\le 4$

${{\left( 1 \right)}^{2}}=1\le 4$

${{\left( 2 \right)}^{2}}=4\le 4$

$\therefore $The set $C=\left\{ x:x\text{In roaster form, the order in which the elements is an integer;}{{\text{x}}^{2}}\le 4 \right\}$ contains elements such as $\left\{ -2,-1,0,1,2 \right\}$


iv. $D=\left\{ x:x\text{ is a letter in the word ''LOYAL''} \right\}$

Ans:

Given that,

$D=\left\{ x:x\text{ is a letter in the word ''LOYAL''} \right\}$

To list the elements of the given set

There are $5$ total letters in the given word in which L gets repeated two times.

So the elements in the set are $\left\{ L,O,Y,A \right\}$

$\therefore $The set $D=\left\{ x:x\text{ is a letter in the word ''LOYAL''} \right\}$ consists the elements $\left\{ L,O,Y,A \right\}$.


v. $E=\left\{ x:x\text{ is a month of a year not having 31 days} \right\}$

Ans:

Given that,

$E=\left\{ x:x\text{ is a month of a year not having 31 days} \right\}$

To list the elements of the given set

The months that don’t have $31$ are as follows:

February, April, June, September, November

$\therefore $The set $E=\left\{ x:x\text{ is a month of a year not having 31 days} \right\}$ consist of the elements such that $\left\{ \text{February, April, June, September, November} \right\}$


vi. $F=\left\{ x:x\text{ is a consonant in the English alphabet which precedes k} \right\}$

Ans:

Given that,

$F=\left\{ x:x\text{ is a consonant in the English alphabet which precedes k} \right\}$

To list the elements of the given set

The consonants are letters in English alphabet other than vowels such as a, e, i, o, u and the consonants that precedes k include b, c, d, f, g, h, j

$\therefore $The set $F=\left\{ x:x\text{ is a consonant in the English alphabet which precedes k} \right\}$ consists of the set $\left\{ b,c,d,f,g,h,j \right\}$


6. Match each of the sets on the left in the roaster form with the same set on the right described inn set-builder form.

i. $\left\{ 1,2,3,6 \right\}$

Ans:

Given that,

$\left\{ 1,2,3,6 \right\}$

To match the roaster form in the left with the set builder form in the right

In roaster form, the order in which the elements are listed is immaterial.

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

It has been observed from the set that these set of numbers are the set of natural numbers which are also the divisors of $6$

Thus, $\left\{ 1,2,3,6 \right\}=\left\{ x:x\text{ is a natural number and is a divisor of 6} \right\}$ is the correct option which is option.


ii. $\left\{ 2,3 \right\}$

Ans:

Given that,

$\left\{ 2,3 \right\}$

To match the roaster form in the left with the set builder form in the right

In roaster form, the order in which the elements are listed is immaterial.

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

It has been observed from the set that these set of numbers are the set of prime numbers which are also the divisors of $6$

Thus, $\left\{ 2,3 \right\}=\left\{ x:x\text{ is a prime number and is a divisor of 6} \right\}$ is the correct option which is option (a)


iii. $\left\{ M,A,T,H,E,I,C,S \right\}$

Ans:

Given that,

$\left\{ M,A,T,H,E,I,C,S \right\}$

To match the roaster form in the left with the set builder form in the right

In roaster form, the order in which the elements are listed is immaterial.

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

It has been observed from the set of these letters of word MATHEMATICS.

Thus, $\left\{ M,A,T,H,E,I,C,S \right\}=\left\{ x:x\text{ is a letter of the word MATHEMATICS} \right\}$ is the correct option which is option (d)


iv. $\left\{ 1,3,5,7,9 \right\}$

Ans:

Given that,

$\left\{ 1,3,5,7,9 \right\}$

To match the roaster form in the left with the set builder form in the right

In roaster form, the order in which the elements are listed is immaterial.

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

It has been observed from the set that these sets of numbers are the set of odd numbers that are less than $10$.

Thus, $\left\{ 1,3,5,7,9 \right\}=\left\{ x:x\text{ is a odd number less than 10} \right\}$ is the correct option which is option (b)

Conclusion

In conclusion, 11th Math 1 Exercise 1.1 has introduced students to the fundamental concepts of sets, including their definitions, types, and notations. Understanding these basics is crucial as they form the foundation for more complex topics in mathematics. By completing this class 11 maths exercise 1.1, students now have a solid grasp of what sets are and how they are used in mathematics. This knowledge will be invaluable as students progress through students studies, helping students tackle more advanced problems with confidence. 


Class 11 Maths Chapter 1: Exercises Breakdown

Exercise

Number of Questions

Exercise 1.2

6 Questions & Solutions

Exercise 1.3

8 Questions & Solutions 

Exercise 1.4

12 Questions & Solutions

Exercise 1.5

7 Questions & Solutions 

Miscellaneous Exercise

10 Questions & Solutions 

 

CBSE Class 11 Maths Chapter 1 Other Study Materials


Chapter-Specific NCERT Solutions for Class 11 Maths

Given below are the chapter-wise NCERT Solutions for Class 11 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.



Important Related Links for CBSE Class 11 Maths

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FAQs on NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1

1. What foundational concepts are introduced in the NCERT Solutions for Class 11 Maths Chapter 1 Sets?

NCERT Solutions for Class 11 Maths Chapter 1 Sets introduce essential ideas such as the definition of sets, ways to represent sets (roster and set-builder forms), and different types of sets like finite, infinite, singleton, null, and equal sets. Understanding these basics is key because they form the underpinning for later chapters in mathematics as per the 2025–26 CBSE syllabus.

2. How does Exercise 1.1 help develop set notation skills in Maths Class 11?

Exercise 1.1 strengthens students’ ability to use set notations such as curly brackets { }, the element symbol ∈, and set-builder versus roster forms. It also teaches how to identify well-defined collections and use mathematical symbols correctly, following the CBSE 2025–26 guidelines.

3. What criteria determine whether a collection is a set in Class 11 Maths?

A collection is a set if all its elements are well-defined and distinct. This means every object of the set can be clearly identified—ambiguous or subjective criteria (like 'best' or 'most talented') mean the collection is not a valid set, as clarified in NCERT Solutions for Chapter 1 Sets.

4. What are the most common errors students make when listing elements of sets?

Students often make errors by repeating elements, including ill-defined items, or confusing order and representation. For example, in set roster form, repetition is not allowed, and order does not matter. The NCERT Solutions stress these CBSE norms to avoid such mistakes.

5. How are finite and infinite sets identified as per Class 11 Sets NCERT Solutions?

A finite set has a countable, specific number of elements, e.g., {1, 2, 3, 4, 5}. An infinite set has unlimited elements, such as {1, 2, 3, ...}. Exercise 1.1 of Maths Class 11 Chapter 1 trains students to recognize and explain both types with examples.

6. Why is set-builder form important in Class 11 Maths Chapter 1 NCERT Solutions?

Set-builder form allows students to define sets by a common property rather than listing all elements, which is crucial for working with large or infinite sets. This method is emphasized in both theoretical questions and solved examples in the NCERT Solutions.

7. What types of sets are specifically covered in Exercise 1.1 of NCERT Solutions for Sets?

Exercise 1.1 covers finite, infinite, singleton, null (empty), and equal sets. Each type is defined and applied in questions to ensure conceptual clarity as per CBSE Class 11 requirements.

8. In which scenarios do students confuse sets with non-sets in Chapter 1?

Students often misidentify collections defined by subjective qualities (like 'beautiful paintings') as sets. The NCERT Solutions clarify that only well-defined and objective collections qualify as sets under CBSE standards.

9. What is the notation for an empty set according to NCERT Solutions for Class 11 Sets?

The empty set (or null set) is represented by { } or the symbol ∅. It is a set that contains no elements, and this notation is standardized in Class 11 CBSE Maths as per the latest syllabus.

10. How do the NCERT Solutions for Class 11 Maths guide students in symbol usage within set theory?

NCERT Solutions ensure students use precise symbols:

  • Curly brackets { } to denote sets
  • ∈ for ‘element of’
  • ∉ for ‘not an element of’
  • ⊂ for ‘subset of’
  • ⊃ for ‘superset of’
Correct symbol usage is repeatedly reinforced throughout all exercises in Chapter 1 Sets.

11. What methods are recommended for converting a set from roster to set-builder form in the Class 11 Maths syllabus?

To convert from roster to set-builder form, students should identify the common property linking all listed elements and express it as a mathematical condition, following CBSE guidelines. For example, {2, 4, 6, ...} becomes {x : x is an even natural number}.

12. How does mastering Chapter 1 Sets benefit students in later Class 11 Maths chapters?

Sets form the foundational language for almost all advanced topics, such as functions, relations, probability, and calculus. Mastery of set theory, as developed by NCERT Solutions for Class 11 Maths, is crucial for understanding union, intersection, complements, and mappings in later chapters.

13. What is a singleton set as explained in NCERT Solutions Class 11 Sets?

A singleton set is a set containing exactly one element, such as {5}. The concept and examples are provided in detail in the exercise solutions for Chapter 1 Sets.

14. How many exercises are there in NCERT Class 11 Maths Chapter 1 Sets, and what are their focus areas?

CBSE Class 11 Maths Chapter 1 Sets contains 6 exercises (Exercise 1.1 to 1.5 and a Miscellaneous Exercise) with a total of 48+16 questions. Each exercise progressively builds skills from set definitions and representation to operations on sets and their applications.

15. What strategies suggested in NCERT Solutions help students avoid common pitfalls in set theory questions?

Strategies include:

  • Always check for well-definedness when defining a set
  • Avoid repeating elements in roster form
  • Use precise notation
  • Review solved NCERT examples for different cases (finite vs infinite, set-builder vs roster)
  • Practice converting between forms
These help students align with the CBSE Class 11 exam and scoring standards.