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NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 Se...

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 Sets

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September 24, 2025

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 Sets: Mathematics is one of the most important subjects in Class 11 as it builds the base for higher studies in science and engineering fields. It is not just about solving sums but also about developing logical thinking and problem-solving skills. Chapter 1 of Class 11 Maths – Sets – introduces students to a very basic yet essential concept in mathematics. Sets help us understand how to group and organise data. Whether it is about finding the union or intersection of sets or understanding subsets and Venn diagrams, this Class 11 maths ch 1 forms the foundation for topics that will come later in the syllabus.

To help students understand the concepts better, the NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 have been provided below. These NCERT solutions for class 11 maths chapter 1 offer step-by-step explanations for each question so that students can practise well and clear their doubts. The Class 11 Maths Chapter 1 Exercise 1.1 solutions are prepared according to the latest CBSE syllabus and are useful for both school exams and entrance tests. Students can start practicing using Class 11 Maths Ch 1 Ex 1.1, which presents the basic concepts of sets in a way that is clear.

Check Out: Class 11th Books

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 Sets

Below is the NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 Sets -

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

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

(ii) The collection of the ten most talented writers of India.

(iii) A team of eleven best-cricket batsmen of the world.

(iv) The collection of all boys in your class.

(v) The collection of all natural numbers less than 100.

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

(vii) The collection of all even integers.

(viii) The collection of questions in this Chapter.

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

Solution:

(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects, as one can identify a month which belongs to this collection. Therefore, this collection is a set. (ii) The collection of the ten most talented writers of India is not a well-defined collection, as the criteria to determine a writer’s talent may differ from one person to another. Therefore, this collection is not a set. (iii) A team of eleven best-cricket batsmen of the world is not a well-defined collection, as the criteria to determine a batsman’s talent may vary from one person to another. Therefore, this collection is not a set. (iv) The collection of all boys in your class is a well-defined collection, as you can identify a boy who belongs to this collection. Therefore, this collection is a set. (v) The collection of all natural numbers less than 100 is a well-defined collection, as one can find a number which belongs to this collection. Therefore, this collection is a set. (vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined collection, as one can find a book which belongs to this collection. Therefore, this collection is a set. (vii) The collection of all even integers is a well-defined collection, as one can find an integer which belongs to this collection. Therefore, this collection is a set. (viii) The collection of questions in this Chapter is a well-defined collection, as one can find a question which belongs to this chapter. Therefore, this collection is a set. (ix) A collection of the most dangerous animals in the world is not a well-defined collection, as the criteria to find the dangerousness of an animal can differ from one animal to another. Therefore, this collection is not a set.

2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces.

(i) 5…A (ii) 8…A (iii) 0…A

(iv) 4…A (v) 2…A (vi) 10…A

Solution:

(i) 5 ∈ A (ii) 8 ∉ A (iii) 0 ∉ A (iv) 4 ∈ A (v) 2 ∈ A (vi) 10 ∉ A

3. Write the following sets in roster form.

(i) A = { x : x is an integer and –3 < x < 7}.

(ii) B = { x : x is a natural number less than 6}.

(iii) C = { x : x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = { x : x is a prime number which is divisor of 60}.

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

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

Solution:

(i) A = { x : x is an integer and –3 < x < 7} –2, –1, 0, 1, 2, 3, 4, 5, and 6 only are the elements of this set. Hence, the given set can be written in roster form as A = {–2, –1, 0, 1, 2, 3, 4, 5, 6} (ii) B = { x : x is a natural number less than 6} 1, 2, 3, 4, and 5 only are the elements of this set. Hence, the given set can be written in roster form as 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} 17, 26, 35, 44, 53, 62, 71, and 80 only are the elements of this set. Hence, the given set can be written in roster form as C = {17, 26, 35, 44, 53, 62, 71, 80} (iv) D = { x : x is a prime number which is divisor of 60} NCERT Solutions Class 11 Chapter 1 Ex 1.1 Image 1 Here, 60 = 2 × 2 × 3 × 5 2, 3 and 5 only are the elements of this set. Hence, the given set can be written in roster form as D = {2, 3, 5} (v) E = The set of all letters in the word TRIGONOMETRY TRIGONOMETRY is a 12 letters word out of which T, R and O are repeated. Hence, the given set can be written in roaster form as E = {T, R, I, G, O, N, M, E, Y} (vi) F = The set of all letters in the word BETTER BETTER is a 6 letters word out of which E and T are repeated. Hence, the given set can be written in roster form as F = {B, E, T, R}

Check Out: Class 11th Question Banks

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

(i) (3, 6, 9, 12)

(ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625}

(iv) {2, 4, 6 …}

(v) {1, 4, 9 … 100}

Solution:

(i) {3, 6, 9, 12} The given set can be written in the set-builder form as { x : x = 3 n , n ∈ N and 1 ≤ n ≤ 4}. (ii) {2, 4, 8, 16, 32} We know that 2 = 2 1 , 4 = 2 2 , 8 = 2 3 , 16 = 2 4 , and 32 = 2 5 . Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as { x : x = 2 n , n ∈ N and 1 ≤ n ≤ 5}. (iii) {5, 25, 125, 625} We know that 5 = 5 1 , 25 = 5 2 , 125 = 5 3 , and 625 = 5 4 . Therefore, the given set {5, 25, 125, 625} can be written in the set-builder form as { x : x = 5 n , n ∈N and 1 ≤ n ≤ 4}. (iv) {2, 4, 6 …} {2, 4, 6 …} is a set of all even natural numbers. Therefore, the given set {2, 4, 6 …} can be written in the set-builder form as { x : x is an even natural number}. (v) {1, 4, 9 … 100} We know that 1 = 1 2 , 4 = 2 2 , 9 = 3 2 …100 = 10 2 . Therefore, the given set {1, 4, 9… 100} can be written in the set-builder form as { x : x = n 2 , n ∈ N and 1 ≤ n ≤ 10}.

5. List all the elements of the following sets.

(i) A = { x : x is an odd natural number}

(ii) B = { x : x is an integer, -1/2 < x < 9/2}

(iii) C = { x : x is an integer, x 2 ≤ 4}

(iv) D = { x : x is a letter in the word “LOYAL”}

(v) E = { x : x is a month of a year not having 31 days}

(vi) F = { x : x is a consonant in the English alphabet which proceeds k }

Solution:

(i) A = { x : x is an odd natural number} So, the elements are A = {1, 3, 5, 7, 9 …..}. (ii) B = { x : x is an integer, -1/2 < x < 9/2} We know that – 1/2 = – 0.5 and 9/2 = 4.5 So, the elements are B = {0, 1, 2, 3, 4}. (iii) C = { x : x is an integer, x 2 ≤ 4} We know that (–1) 2 = 1 ≤ 4; (–2) 2 = 4 ≤ 4; (–3) 2 = 9 > 4 Here, 0 2 = 0 ≤ 4, 1 2 = 1 ≤ 4, 2 2 = 4 ≤ 4, 3 2 = 9 > 4 So, we get C = {–2, –1, 0, 1, 2} (iv) D = { x : x is a letter in the word “LOYAL”} So, the elements are D = {L, O, Y, A} (v) E = { x : x is a month of a year not having 31 days} So, the elements are E = {February, April, June, September, November} (vi) F = { x : x is a consonant in the English alphabet which proceeds k } So, the elements are F = {b, c, d, f, g, h, j}

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

(i) {1, 2, 3, 6} (a) {x: x is a prime number and a divisor of 6}

(ii) {2, 3} (b) {x: x is an odd natural number less than 10}

(iii) {M, A, T, H, E, I, C, S} (c) {x: x is a natural number and divisor of 6}

(iv) {1, 3, 5, 7, 9} (d) {x: x is a letter of the word MATHEMATICS}

Solution:

(i) Here, the elements of this set are natural numbers as well as divisors of 6. Hence, (i) matches with (c). (ii) 2 and 3 are prime numbers which are divisors of 6. Hence, (ii) matches with (a). (iii) The elements are the letters of the word MATHEMATICS. Hence, (iii) matches with (d). (iv) The elements are odd natural numbers which are less than 10. Hence, (v) matches with (b).

Check Out: CBSE Question Bank Class 11 Mathematics Chapter-wise and Topic-wise

Summary of Class 11 Maths Chapter 1

What is a Set?

A set is a collection of well-defined and distinct objects or elements. These elements can be numbers, letters, or even names. For example, the set of vowels in the English alphabet is written as A = {a, e, i, o, u}.

Representation of Sets

Sets can be represented in two major forms:

Roster Form: All the elements are listed, separated by commas and enclosed in curly brackets.

Example: B = {2, 4, 6, 8}

Set-Builder Form: Describes a rule or property that all elements of the set follow.

Example: B = {x : x is an even number less than 10}

Types of Sets

Empty Set: A set with no elements. Example: {}
Finite and Infinite Sets: Sets with a countable number of elements are finite; those without an end are infinite.
Equal Sets: Sets with exactly the same elements.
Singleton Set: A set with only one element.
Subset and Superset: If every element of Set A is also in Set B, then A is a subset of B.

Also Check, CBSE Class 11 Formula Handbook For 2026 Exams

Venn Diagrams

Venn diagrams are used to visually show the relationships between different sets using circles. They help us understand how sets overlap, relate, or differ from each other.

Operations on Sets

Union (A ∪ B): Combines all elements from both sets without repetition.
Intersection (A ∩ B): Contains only the elements common to both sets.
Difference (A – B): Elements that are in A but not in B.
Complement (A′): All elements in the universal set that are not in A.

Properties of Set Operations

The chapter also explains important properties like:

Commutative Law: A ∪ B = B ∪ A
Associative Law: (A ∪ B) ∪ C = A ∪ (B ∪ C)
Distributive Law: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
De Morgan’s Laws:

(A ∪ B)' = A' ∩ B'

(A ∩ B)' = A' ∪ B'

Universal Set and Power Set

Universal Set: The set that contains all the elements under consideration. Denoted by 'U'.
Power Set: The collection of all subsets of a given set, including the empty set and the set itself.

Practical Applications of Sets

The concept of sets is used in many areas like probability, statistics, logic, computer science, and database systems. It helps in organising data, solving puzzles, and analysing relationships between groups.