NCERT Solutions for Class 11 Mathematics Chapter 1
NCERT solutions for Class 11 Mathematics Chapter 1 Sets – complete answers & explanations
This blog provides clear and reliable NCERT solutions for Class 11 Mathematics Chapter 1 Sets. This chapter introduces students to the fundamental idea of sets, which is one of the most important building blocks in mathematics. It helps learners understand how to define, represent, and work with collections of objects in a structured way. Mastering this chapter is essential because it supports many advanced topics in algebra, probability, and logic. These solutions guide students step-by-step so they can learn the correct approach to answering questions and improve their accuracy. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.
What this NCERT chapter covers?
1. Introduction to sets and how
they are defined in mathematics
2. Different types of sets such as null, finite, and infinite sets
3. Methods of representing sets using roster form and set-builder form
4. Understanding subsets, equal sets, and universal sets
5. Learning symbols like ∈, ∉, ⊂, and ⊄ and their correct usage
6. Performing operations on sets such as union, intersection, and complement
7. Concept of intervals and their representation on number lines
8. Identifying relationships between different sets
9. Solving practical problems using set concepts
10. Understanding disjoint sets and complement of sets
11. Applying properties of sets in problem-solving
12. Building logical thinking and problem-solving skills for exams
How to use these NCERT solutions?
1. Start by reading each question
carefully from the worksheet before attempting it
2. Try solving the questions on your own to test your understanding
3. Use the solutions to check your answers step-by-step
4. Compare your approach with the correct answers to identify mistakes
5. Focus on understanding where you went wrong and improve accordingly
6. Practice writing answers neatly using proper mathematical notation
7. Parents and teachers can guide students by explaining difficult concepts
8. Follow the solutions in the same order as given in the worksheet
9. Revise regularly to strengthen concepts and improve speed
10. Use these solutions as a support tool, not a replacement for practice
Important tips & tricks for students
1. Always read the question carefully before starting your answer
2. Do not confuse elements with subsets
3. Practice writing sets in both roster and set-builder forms
4. Revise symbols like ∈, ∉, ⊂, ⊄ regularly
5. Avoid skipping steps in set operations
6. Be clear about the difference between finite and infinite sets
7. Pay attention to interval notation and boundary values
8. Practice identifying union and intersection correctly
9. Follow instructions properly for activity-based or open-ended questions
10. Keep your answers neat and structured to score full marks
NCERT solutions – complete answer key
EXERCISE 1.1
Which of the following are sets ? Justify your answer.
(i) Set
(ii) Not a set
(iii) Not a set
(iv) Set
(v) Set
(vi) Set
(vii) Set
(viii) Set
(ix) Not a set
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces:
(i) ∈
(ii) ∉
(iii) ∉
(iv) ∈
(v) ∈
(vi) ∉
Write the following sets in roster form:
(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}
Write the following sets in the set-builder form :
(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}
List all the elements of the following sets :
(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}
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
1 – c
2 – a
3 – d
4 – b
EXERCISE 1.2
Which of the following are examples of the null set.
(i) Null set
(ii) Not null set
(iii) Null set
(iv) Null set
Which of the following sets are finite or infinite.
(i) Finite
(ii) Infinite
(iii) Finite
(iv) Infinite
(v) Finite
State whether each of the following set is finite or infinite:
(i) Infinite
(ii) Finite
(iii) Infinite
(iv) Finite
(v) Infinite
In the following, state whether A = B or not:
(i) A = B
(ii) A ≠ B
(iii) A = B
(iv) A ≠ B
Are the following pair of sets equal ? Give reasons.
(i) Not equal
(ii) Equal
From the sets given below, select equal sets:
Equal sets: B and D, E and G
EXERCISE 1.3
Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces :
(i) ⊂
(ii) ⊄
(iii) ⊂
(iv) ⊄
(v) ⊄
(vi) ⊂
(vii) ⊂
Examine whether the following statements are true or false:
(i) True
(ii) True
(iii) False
(iv) True
(v) True
(vi) True
Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
(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.
Write down all the subsets of the following sets.
(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
Write the following as intervals :
(i) (–4, 6]
(ii) (–12, –10)
(iii) [0, 7)
(iv) [3, 4]
Write the following intervals in set-builder form :
(i) {x : –3 < x < 0}
(ii) {x : 6 ≤ x ≤ 12}
(iii) {x : 6 < x ≤ 12}
(iv) {x : –23 ≤ x < 5}
What universal set(s) would you propose for each of the following :
(i) Set of all triangles
(ii) Set of all triangles
Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C.
(i), (iii)
EXERCISE 1.4
Find the union of each of the following pairs of sets :
(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}
Let A = { a, b }, B = {a, b, c}. Is A ⊂ B ? What is A ∪ B ?
Yes, A ⊂ B
A ∪ B = {a, b, c}
If A and B are two sets such that A ⊂ B, then what is A ∪ B ?
A ∪ B = B
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = {7, 8, 9, 10 }; find.
(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}
Find the intersection of each pair of sets of question 1 above.
(i) {1,3}
(ii) {a}
(iii) {3}
(iv) {6}
(v) φ
If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}and D = {15, 17}; find.
(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}
If A = {x : x is a natural number }, B = {x : x is an even natural number} C = {x : x is an odd natural number}andD = {x : x is a prime number }, find.
(i) even natural numbers
(ii) odd natural numbers
(iii) prime numbers
(iv) φ
(v) prime even numbers
(vi) odd prime numbers
Which of the following pairs of sets are disjoint.
(i) Not disjoint
(ii) Not disjoint
(iii) Disjoint
If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = {2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }; find.
(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}
If X= { a, b, c, d } and Y = { f, b, d, g}, find.
(i) {a, c}
(ii) {f, g}
(iii) {b, d}
If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
Irrational numbers
State whether each of the following statement is true or false. Justify your answer.
(i) False
(ii) False
(iii) True
(iv) True
Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }. Find.
(i) {5,6,7,8,9}
(ii) {1,3,5,7,9}
(iii) {1,2,7,8,9}
(iv) {1,5,7,9}
(v) {1,2,3,4}
(vi) {1,2,3,4,7,8,9}
EXERCISE 1.5
If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :
(i) {d, e, f, g, h}
(ii) {a, b, c, h}
(iii) {b, d, f, h}
(iv) {b, c, d, e}
Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(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
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that.
(i) LHS = RHS
(ii) LHS = RHS
Draw appropriate Venn diagram for each of the following :
(i) (A ∪ B)′
(ii) A′ ∩ B′
(iii) (A ∩ B)′
(iv) A′ ∪ B′
Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?
Set of all equilateral triangles.
Decide, among the following sets, which sets are subsets of one and another:
A ⊂ B, A ⊂ C
D ⊂ A, D ⊂ B, D ⊂ C
B ⊂ C
Fill in the blanks to make each of the following a true statement :
(i) U
(ii) U
(iii) φ
(iv) φ
MISCELLANEOUS EXERCISE ON CHAPTER 1
In each of the following, determine whether the statement is true or false.
(i) False
(ii) False
(iii) True
(iv) False
(v) False
(vi) True
Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.
B = C
Show that the following four conditions are equivalent :
(i) ⇔ (ii) ⇔ (iii) ⇔ (iv)
Show that if A ⊂ B, then C – B ⊂ C – A.
C – B ⊂ C – A
Show that for any sets A and B,
A = (A ∩ B) ∪ (A – B)
A ∪ (B – A) = (A ∪ B)
Using properties of sets, show that.
(i) A
(ii) A
Show that A ∩ B = A ∩ C need not imply B = C.
Not necessary.
Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B.
(Hints A = A ∩ ( A ∪ X ) , B = B ∩ ( B ∪ X ) and use Distributive law )
Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = φ.
A = {1, 2}
B = {2, 3}
C = {1, 3}
A = B
Why NCERT solutions help students?
These NCERT solutions help students prepare effectively for exams by providing clear and reliable answers. They improve concept clarity, ensure alignment with the NCERT pattern, and build confidence while solving similar questions.
Help your child build strong Mathematics fundamentals with expert-guided learning support.