Sets Exercise 1.1 of Class 11 NCERT Mathematics is the starting point for understanding the fundamental concepts of set theory. In this exercise, students learn how to define sets, represent them using roster form and set-builder form, and identify elements of well-defined collections. It builds the base for advanced topics like subsets, set operations, and Venn diagrams. This section also includes a variety of solved examples, NCERT-based questions, and practice problems to strengthen conceptual clarity. It is highly useful for school exams as well as competitive exams of India.
Chapter 1 SETS Exercise 1.1 NCERT Solutions for Class 11 Maths
NCERT Question 1 : Which of the following are sets? Justify our answer
(i) The collection of all the months of a year beginning with the letter J.
(ii) The collection of 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 most dangerous animals of the world
Solution :
(i) The collection of all months of a year beginning with the letter J.
All months that begins with the letter J is a well-defined collection as one can easily identify whether a month begins with J or not.
Therefore, this collection is a set.
(ii) The collection of ten most talented writers of India.
Ten most talented writers of India is not a well-defined collection as one writer’s talent cannot be measured and it vary for person to person.
Therefore, this collection is not a set.
(iii) A team of eleven best-cricket batsmen of the world.
A team of eleven best cricket batsmen of the world is not a well-defined collection because one person can consider a batsman as best whereas other person may not consider it. There’s no measuring unit.
Therefore, this collection is not a set.
(iv) The collection of all boys in your class.
This collection is a well-defined collection as you can easily identify whether a boy belongs to your class or not.
Therefore, this collection is a set.
(v) The collection of all natural numbers less than 100.
The collection of all natural numbers less than $100$ is a well-defined collection because it’s possible to decide whether a number is less than $100$ or not.
Therefore, this collection is a set.
(vi) A collection of novels written by the writer Munshi Prem Chand.
A collection of novels written by the writer “Munshi Prem Chand” is a well-defined collection because one can definitely identify whether a book is written by “Munshi Prem Chand” or not.
Therefore, this collection is a set.
(vii) The collection of all even integers.
This collection is a well-defined collection because one can definitely identify which is an even integer and which is not.
Therefore, this collection is a set.
(viii) The collection of questions in this Chapter.
This collection is a well-defined collection because one can definitely identify whether a question belongs to this chapter or not.
Therefore, this collection is a set.
(ix) A collection of most dangerous animals of the world.
This collection of most dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal varies from person to person.
Therefore, this collection is not a set.
NCERT Question 2: Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
(i) $5\ \ldots\ A$
(ii) $8\ \ldots\ A$
(iii) $0\ \ldots\ A$
(iv) $4\ \ldots\ A$
(v) $2\ \ldots\ A$
(vi) $10\ \ldots\ A$
Solution:
(i) $5 \in A$
(ii) $8 \notin A$
(iii) $0 \notin A$
(iv) $4 \in A$
(v) $2 \in A$
(vi) $10 \notin A$
NCERT Question 3: Write the following sets in roster form:
(i) $A = {x: x \text{ is an integer and } -3 < x < 7}.$
(ii) $B = {x: x \text{ is a natural number less than }6}.$
(iii) $C = {x: x \text{ is a two-digit natural number such that the\\ sum of its digits is }8}$
(iv) $D = {x: x \text{ is a prime number which is divisor of }60}.$
(v) $E =$ The set of all letters in the word TRIGONOMETRY.
(vi) $F =$ The set of all letters in the word BETTER.
Solution:
(i)
$$A = \{-2,-1,0,1,2,3,4,5,6\}$$
(ii)
$$B = \{1,2,3,4,5\}$$
(iii)
$$C = \{80, 71 ,62, 53, 44, 26, 35, 17\}$$
(iv) Prime factorization of $60$ is
$$60 = 2^2 \times 3 \times 5$$
$$D = \{2 ,3 ,5\}$$
(v)
$$E = \{Y ,E ,M ,N ,O ,G ,I ,R ,T\}$$
(vi)
$$F = \{R ,T ,E ,B\}$$
NCERT Question 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) $3=3\cdot1,\ 6=3\cdot2,\ 9=3\cdot3,\ 12=3\cdot4.$
$$\therefore\ \{3,6,9,12\}=\{x:\ x=3n,\ n\in\mathbb{N}\ \text{and}\ 1\le n\le 4\}$$
(ii) $2=2^1,\ 4=2^2,\ 8=2^3,\ 16=2^4,\ 32=2^5.$
$$\therefore\ \{2, 4, 8, 16, 32\}=\{x:\ x=2^n,\ n\in\mathbb{N}\ \text{and}\ 1\le n\le 5\}$$
(iii) $5=5^1,\ 25=5^2,\ 125=5^3,\ 625=5^4.$
$$\therefore\ \{5, 25, 125, 625\}=\{x:\ x=5^n,\ n\in\mathbb{N}\ \text{and}\ 1\le n\le 4\}$$
(iv) Given set is a set of all even natural numbers.
$$\therefore\ \{2, 4, 6,\dots\}=\{x:\ x \text{ is an even natural number\}}$$
(v) $1=1^2,\ 4=2^2,\ 9=3^2,\ \dots,\ 100=10^2.$
$$\therefore\ \{1, 4, 9,\dots,100\}=\{x:\ x=n^2,\ n\in\mathbb{N}\ \text{and}\ 1\le n\le 10\}$$
NCERT Question 5: List all the elements of the following sets:
(i) $A = \{x: x \text{ is an odd natural number}\}$
(ii) $B = \{x: x \text{ is an integer, } -\tfrac{1}{2} < x < \tfrac{9}{2}\}$
(iii) $C =\{x: x \text{ is an integer, } x^2 \le 4\}$
(iv) $D = \{x: x \text{ is a letter in the word “LOYAL”}\}$
(v) $E = \{x: x \text{ is a month of a year not having }31\text{ days}\}$
(vi) $F =\{x: x \text{ is a consonant in the English alphabet \\which precedes }k\}$
Solution:
(i)
$$A = \{1, 3, 5, 7, 9,\dots\}$$
(ii) Integers satisfying $-\tfrac{1}{2}<x<\tfrac{9}{2}$ are $0,1, 2, 3, 4$
$$B = \{0, 1, 2, 3, 4\}$$
(iii) Check integers:
$$(-1)^2=1\le4,\quad (-2)^2=4\le4,\quad (-3)^2=9>4$$
$$0^2=0\le4,\quad 1^2=1\le4,\quad 2^2=4\le4,\quad 3^2=9>4$$
$$\therefore\ C = \{-2, -1, 0, 1, 2\}$$
(iv)
$$D = \{L, O, Y, A\}$$
(v)
$$E = \{\text{February, April, June, September, November}\}$$
(vi)
$$F = \{b, c, d, f, g, h, j\}$$
NCERT Question 6: Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
(i) $\{1, 2, 3, 6\}$
(a) $\{x:\ x \text{ is a prime number and a divisor of }6\}$
(ii) $\{2, 3\}$
(b) $\{x:\ x \text{ is an odd natural number less than }10\}$
(iii) $\{M, A,T, H,E, I, C, S\}$
(c) $\{x:\ x \text{ is natural number and divisor of }6\}$
(iv) $\{1, 3, 5, 7, 9\}$
(d) $\{x:\ x \text{ is a letter of the word MATHEMATICS}\}$
Solution:
(i) All the elements given in this set are natural numbers as well as the divisors of $6$.
Therefore, (i) matches with (c).
(ii) We know that $2$ and $3$ are prime numbers. They are also the divisors of $6$.
Therefore, (ii) matches with (a).
(iii) This set contains all the letters from the word MATHEMATICS.
Therefore, (iii) matches with (d).
(iv) This set contains odd natural numbers which are smaller than $10$.
Therefore, (iv) matches with (b).
Important Chapter Links
Sets Exercise 1.1 of Class 11 NCERT Mathematics introduces the basic concepts of sets, including definition, representation (roster form and set-builder form), and identification of elements. This exercise helps build a strong foundation for understanding advanced topics in set theory and is important for school exams as well as competitive exams like JEE.
FAQs of Chapter-1 Sets Exercise 1.1 NCERT Solutions for Class 11 Maths
What is Exercise 1.1 in Sets about?
Exercise 1.1 focuses on the basic definition of sets, their representation in roster and set-builder forms, and identification of elements.
What is a well-defined set?
A well-defined set is one where it is clear whether an element belongs to the set or not.
What is roster form of a set?
Roster form lists all elements of a set explicitly inside curly brackets : A = {1, 2, 3}
What is set-builder form?
Set-builder form describes a set using a property : A = {x : x { satisfies a given condition }
Why is Exercise 1.1 important?
It forms the foundation for all topics in set theory and is essential for both CBSE exams and competitive exams.
How can I convert roster form to set-builder form?
Identify the common property of elements and express it using a condition.
Is Exercise 1.1 important for JEE?
Yes, basic concepts from this exercise are used in advanced problems in JEE and other exams.
Are NCERT solutions enough for preparation?
NCERT solutions are essential, but additional practice with MCQs and PYQs improves performance.
What type of questions are asked in Exercise 1.1?
Questions mainly involve writing sets in different forms and identifying elements.
Can beginners easily understand this exercise?
Yes, it is designed as an introductory exercise and is easy to understand with proper practice.