NCERT Solutions for Class 11 Mathematics Chapter 1 Sets
NCERT Solutions for Class 11 Mathematics Chapter 1 Sets
NCERT Solutions for Class 11 Mathematics Chapter 1 Sets
This worksheet provides complete and accurate NCERT Solutions for Class 11 Mathematics Chapter 1 Sets. This chapter introduces students to the fundamental concept of sets, which forms the basis of many topics in mathematics. Students learn how to define sets, represent them in different forms, and understand relationships between sets. This chapter is important because it builds a strong foundation for advanced topics like relations, functions, and probability. The worksheet follows the NCERT structure and includes clear answers to all exercises for better understanding and practice.
Chapter summary: stories, poems & themes
This chapter is concept-based and does not include stories or poems. It focuses on understanding mathematical concepts related to sets through definitions, examples, and exercises. Students learn how to identify sets, write them in roster and set-builder forms, and perform operations like union, intersection, and complement. The chapter also includes activity-based learning through classification, matching, and reasoning questions.
What this NCERT chapter covers?
• Understanding the concept of sets and their representation
• Writing sets in roster form and set-builder form
• Identifying elements and types of sets such as finite, infinite, and null sets
• Learning subset, equal sets, and universal sets
• Performing operations like union and intersection
• Understanding complements and Venn diagrams
• Developing logical thinking through true/false and reasoning-based questions
How to use these NCERT solutions?
Students should first try solving each question on their own before referring to the solutions. After attempting, they can use these answers to check their correctness and understand the proper method. Parents and teachers can use this worksheet to guide students step-by-step as per NCERT standards. The solutions are arranged in the same order as the NCERT textbook, which helps in structured learning, revision, and exam preparation.
Student tips & learning tricks
• Carefully understand the difference between element and subset
• Practice writing sets in both roster and set-builder forms
• Pay attention to symbols like ∈, ∉, ⊂, and ⊄
• Avoid confusing empty set with a set containing zero
• Revise definitions regularly to improve accuracy in answers
• Practice Venn diagrams to better understand set operations
Why NCERT solutions are important?
NCERT Solutions help students learn concepts in a clear and structured way as per the CBSE curriculum. They ensure that students follow the correct methods and terminology expected in exams. These solutions strengthen conceptual understanding, improve problem-solving skills, and boost confidence. Regular practice using NCERT-based answers helps students perform better in school assessments and competitive exams.
Complete answer key – NCERT solutions
EXERCISE 1.1
1.
(i) Set
(ii) Not a set
(iii) Not a set
(iv) Set
(v) Set
(vi) Set
(vii) Set
(viii) Set
(ix) Not a set
2.
(i) ∈
(ii) ∉
(iii) ∉
(iv) ∈
(v) ∈
(vi) ∉
3.
(i) {–3, –2, –1, 0, 1, 2, 3, 4, 5, 6}
(ii) {1, 2, 3, 4, 5}
(iii) {17, 26, 35, 44, 53, 62, 71, 80}
(iv) {2, 3, 5}
(v) {T, R, I, G, O, N, M, E, Y}
(vi) {B, E, T, R}
4.
(i) {x : x = 3n, n ∈ N}
(ii) {x : x = 2ⁿ, n ∈ N}
(iii) {x : x = 5ⁿ, n ∈ N}
(iv) {x : x is an even natural number}
(v) {x : x = n², 1 ≤ n ≤ 10}
5.
(i) {1, 3, 5, 7, 9, ...}
(ii) {0, 1, 2, 3, 4}
(iii) {–2, –1, 0, 1, 2}
(iv) {L, O, Y, A}
(v) {February, April, June, September, November}
(vi) {b, c, d, f, g, h, j}
6.
1 – c
2 – a
3 – d
4 – b
EXERCISE 1.2
1.
(i) Null set
(ii) Not null set
(iii) Null set
(iv) Null set
2.
(i) Finite
(ii) Infinite
(iii) Finite
(iv) Infinite
(v) Finite
3.
(i) Infinite
(ii) Finite
(iii) Infinite
(iv) Finite
(v) Infinite
4.
(i) A = B
(ii) A ≠ B
(iii) A = B
(iv) A ≠ B
5.
(i) Not equal
(ii) Equal
6.
Equal sets: B and D, E and G
EXERCISE 1.3
1.
(i) ⊂
(ii) ⊄
(iii) ⊂
(iv) ⊄
(v) ⊄
(vi) ⊂
(vii) ⊂
2.
(i) True
(ii) True
(iii) False
(iv) True
(v) True
(vi) True
3.
(i) {3, 4} ⊂ A
Reason: 3 and 4 are not individual elements of A; only {3,4} is an element.
(iii) {{3, 4}} ⊂ A
Reason: {3,4} ∈ A but {{3,4}} is not an element of A.
(v) 1 ⊂ A
Reason: 1 is an element, not a set.
(vii) {1, 2, 5} ∈ A
Reason: {1,2,5} is not an element of A; only 1, 2, 5 are elements.
(viii) {1, 2, 3} ⊂ A
Reason: 3 is not an element of A.
(ix) φ ∈ A
Reason: empty set is not an element of A.
(xi) {φ} ⊂ A
Reason: φ is not an element of A.
4.
(i) φ, {a}
(ii) φ, {a}, {b}, {a, b}
(iii) φ, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}
(iv) φ
5.
(i) (–4, 6]
(ii) (–12, –10)
(iii) [0, 7)
(iv) [3, 4]
6.
(i) {x : –3 < x < 0}
(ii) {x : 6 ≤ x ≤ 12}
(iii) {x : 6 < x ≤ 12}
(iv) {x : –23 ≤ x < 5}
7.
(i) Set of all triangles
(ii) Set of all triangles
8.
(i), (iii)
EXERCISE 1.4
1.
(i) {1, 2, 3, 5}
(ii) {a, e, i, o, u, b, c}
(iii) {1, 2, 3, 4, 5, 6, 9, 12, ...}
(iv) {2, 3, 4, 5, 6, 7, 8, 9}
(v) {1, 2, 3}
2.
Yes, A ⊂ B
A ∪ B = {a, b, c}
3.
A ∪ B = B
4.
(i) {1,2,3,4,5,6}
(ii) {1,2,3,4,5,6,7,8}
(iii) {3,4,5,6,7,8}
(iv) {3,4,5,6,7,8,9,10}
(v) {1,2,3,4,5,6,7,8}
(vi) {1,2,3,4,5,6,7,8,9,10}
(vii) {3,4,5,6,7,8}
5.
(i) {1,3}
(ii) {a}
(iii) {3}
(iv) {6}
(v) φ
6.
(i) {7,9,11}
(ii) {11,13}
(iii) φ
(iv) {11}
(v) φ
(vi) {7,9,11}
(vii) φ
(viii) {7,9,11}
(ix) {7,9,11}
(x) {11,13}
7.
(i) even natural numbers
(ii) odd natural numbers
(iii) prime numbers
(iv) φ
(v) prime even numbers
(vi) odd prime numbers
8.
(i) Not disjoint
(ii) Not disjoint
(iii) Disjoint
9.
(i) {3,6,9,15,18,21}
(ii) {3,9,15,18,21}
(iii) {3,6,9,12,18,21}
(iv) {4,8,16,20}
(v) {2,4,8,10,14,16}
(vi) {5,10,20}
(vii) {4,8,16,20}
(viii) {4,8,12,16,20}
(ix) {2,6,10,14}
(x) {5,10,15,20}
(xi) {2,4,6,8,12,14,16}
(xii) {5,10,15,20}
10.
(i) {a, c}
(ii) {f, g}
(iii) {b, d}
11.
Irrational numbers
12.
(i) False
(ii) False
(iii) True
(iv) True
EXERCISE 1.5
1.
(i) {d, e, f, g, h}
(ii) {a, b, c, h}
(iii) {b, d, f, h}
(iv) {b, c, d, e}
2.
(i) odd natural numbers
(ii) even natural numbers
(iii) numbers not multiples of 3
(iv) non-prime numbers
(v) numbers not divisible by both 3 and 5
(vi) non-perfect squares
(vii) non-perfect cubes
(viii) all natural numbers except 3
(ix) all natural numbers except 2
(x) numbers less than 7
(xi) numbers ≤ 4
3.
(i) LHS = RHS
(ii) LHS = RHS
4.
student-generated activity
5.
Set of all equilateral triangles.
6.
A ⊂ B, A ⊂ C
D ⊂ A, D ⊂ B, D ⊂ C
B ⊂ C
7.
(i) U
(ii) U
(iii) φ
(iv) φ
MISCELLANEOUS EXERCISE
1.
(i) False
(ii) False
(iii) True
(iv) False
(v) False
(vi) True
2.
B = C
3.
(i) ⇔ (ii) ⇔ (iii) ⇔ (iv)
4.
C – B ⊂ C – A
5.
A = (A ∩ B) ∪ (A – B)
A ∪ (B – A) = (A ∪ B)
6.
(i) A
(ii) A
7.
Not necessary.
8.
student-generated activity
9.
A = {1, 2}
B = {2, 3}
C = {1, 3}
10.
A = B
Get accurate NCERT Solutions for Class 11 Mathematics Sets chapter and improve your problem-solving skills with step-by-step answers designed for better understanding.