Class 11 maths chapter 1 sets exercise 1.1 | class 11 ch 1 exercise solutions | class 11 chapter 1 exercise solution | sets class 11 ncert solutions | sets class 11 ncert solutions | ncert solution for class 11 maths chapter 1 | ncert exemplar class 11 maths
Looking for NCERT Class 11 Maths Exercise 1.1 solutions? You’ve come to the right place! In this section, we provide complete and easy-to-understand answers to all questions from Exercise 1.1 Class 11 Maths, based on NCERT solutions for Sets – Chapter 1 of Class 11. Whether you’re aiming to build a strong foundation in set theory or preparing for your school exams, these Class 11 Maths Set NCERT solutions are perfect for mastering the basic concepts. View or download the detailed solutions now and strengthen your understanding of sets with clarity and confidence!
sets class 11 ncert solutions || class 11 ch 1 exercise solutions || sets class 11 ncert solutions || class 11 maths chapter 1 sets exercise 1.1 || ncert exemplar class 11 maths || class 11 chapter 1 exercise solution || ncert solution for class 11 maths chapter 1
Exercise 1.1
1A. Which of the following are sets? Justify your answer.
The collection of all the months of a year beginning with the letter J.
The collection of all the months of a year beginning with the letter J.
Answer
Set: Collection of well - defined objects.
There are three months of a year which begins with the letter J, rest of the \(\text{month}^{,}\)s name begin with different letter. So, the given collection has well-defined objects namely January, June and July.
Hence, this collection is a set.
\( \{x: x= \) months of a year beginning with letter \( J\} \)
Alternatively
\(x: x=\) January, June, July where January, June, July are month of a year}
1B. Which of the following are sets? Justify your answer.
The collection of ten most talented writers of India.
The collection of ten most talented writers of India.
Answer
The object of the given collection is quiet subjective and vary with \(\text{person}^{,}\)s personal choice. Some people may be biased toward some as the most talented writers of India whereas for other the list of most talented writers may be altogether different. Hence the given collection \(\text{doesn}^{,}\)t have well defined objects with universal standards.
Hence, this collection is not a set.
1C. Which of the following are sets? Justify your answer.
A team of eleven best-cricket batsmen of the world.
A team of eleven best-cricket batsmen of the world.
Answer
A team of eleven best cricket batsmen of the world is not very clearly defined collection. The cricket team of a nation could be well defined set but best cricket batsmen team would be judge mental and subjective concept varying from person to person.
Hence, this collection is not a set.
1D. Which of the following are sets? Justify your answer.
The collection of all boys in your class.
The collection of all boys in your class.
Answer
The collection of all boys in your class is a well-defined collection because one can definitely differentiate between boys who could belongs to this collection on the basis of appearance itself. The criteria for judging the gender would not vary from person to person. The set has very well defined object which is boys in this class.
Hence, this collection is a set.
sets class 11 ncert solutions || class 11 ch 1 exercise solutions || sets class 11 ncert solutions || class 11 maths chapter 1 sets exercise 1.1 || ncert exemplar class 11 maths || class 11 chapter 1 exercise solution || ncert solution for class 11 maths chapter 1
1E. Which of the following are sets? Justify your answer.
The collection of all natural numbers less than 100.
The collection of all natural numbers less than 100.
Answer
The collection of all natural numbers less than 100 is a well-defined collection because there is no ambiguity in regard of numbers and there values greater than or less than 100 . There are specific numbers which belongs to the given collection. Such numbers choice \(\text{doesn}^{,}\)t vary from person to person. The clearly defined objects make the collection a set.
\( \{x: x=\{0,1,2,3, \ldots 99\} \) where \( \mathrm{n} \in \mathrm{N} \) and \( 0 \leq \mathrm{n} < 100\} \)
N is natural number
1F. Which of the following are sets? Justify your answer.
A collection of novels written by the writer Munshi Prem Chand.
A collection of novels written by the writer Munshi Prem Chand.
Answer
A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because there are finite numbers of books which Munshi Prem Chand has written. The names of the book could not vary from person to person on the basis of personal choice. The well-defined objects of the collection make it a set.
Hence, this collection is a set.
1G. Which of the following are sets? Justify your answer.
The collection of all even integers.
The collection of all even integers.
Answer
The collection of all even integers is a well-defined collection because there \(\text{couldn}^{,}\)t be difference between choosing the even integers from the collection of given numbers or all the numbers taken at a large. The choice will not vary from person to person. The given collection has well-defined objects which meet the universal criteria.
Hence, this collection is a set.
{\( x: x=\ldots-6,-4,-2,0,2,4,6 \ldots \) where n is even integer 2k for some unique integer k}
sets class 11 ncert solutions || class 11 ch 1 exercise solutions || sets class 11 ncert solutions || class 11 maths chapter 1 sets exercise 1.1 || ncert exemplar class 11 maths || class 11 chapter 1 exercise solution || ncert solution for class 11 maths chapter 1
1H. Which of the following are sets? Justify your answer.
The collection of questions in this Chapter.
The collection of questions in this Chapter.
Answer
The collection of the questions in this chapter is a well-defined collection and the set will have well defined objects. One can definitely identify the question that would belong to the collection and could easily number them. The number of questions and the type of questions will not be different for different persons.
Hence the collection is a set.
1I. Which of the following are sets? Justify your answer.
A collection of most dangerous animals of the world.
A collection of most dangerous animals of the world.
Answer
A collection of most dangerous animals of the world is not a very clearly defined set as the ranking of the animals keep on altering and their ranking vary from countries to countries. The objects of the collection are not well-defined and \(\text{doesn}^{,}\)t have universal acceptance as it is.
Hence the collection is not set.
2. Let \( A=\{1,2,3,4,5,6\} \). Insert the appropriate symbol \(\hat a\) or \(\notin \) in the blank spaces:
(i) \( 5 \ldots \mathrm{A} \)
(ii) \( 8 \ldots \mathrm{A} \)
(iii) \( 0 \ldots \mathrm{A} \)
(iv) \( 4 \ldots \mathrm{A} \)
(v) \( 2 \ldots \mathrm{A} \)
(vi) \( 10 \ldots \mathrm{A} \)
(i) \( 5 \ldots \mathrm{A} \)
(ii) \( 8 \ldots \mathrm{A} \)
(iii) \( 0 \ldots \mathrm{A} \)
(iv) \( 4 \ldots \mathrm{A} \)
(v) \( 2 \ldots \mathrm{A} \)
(vi) \( 10 \ldots \mathrm{A} \)
Answer
Here \( \in= \) belongs to
\( \notin= \) does not belongs to
(i) \( 5 \in \mathrm{A} \), since 5 is in the set A
(ii) \( 8 \notin \mathrm{A} \), since 8 is not in the set A
(iii) \( 0 \notin \mathrm{A} \), since 0 is not in the set A
(iv) \( 4 \in A \), since 4 is in the set \( A \)
(v) \( 2 \in A \), since 2 is in the set \( A \)
(vi) \( 10 \notin \mathrm{A} \), since 10 is not in set A
3A. Write the following sets in roster form:
\( \mathrm{A}=\{x: x \) is an integer and \( -3 < x < 7\} \)
\( \mathrm{A}=\{x: x \) is an integer and \( -3 < x < 7\} \)
Answer
Integers are \( -5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9, \ldots\)
The elements of this set are \( -2,-1,0,1,2,3,4,5 \) and 6
The roaster form is
\(A=\{-2,-1,0,1,2,3,4,5,6\}\)
3B. Write the following sets in roster form:
\( B=\{x: x \) is a natural number less than 6\( \} \)
\( B=\{x: x \) is a natural number less than 6\( \} \)
Answer
Here natural numbers are \( =1,2,3,4,5,6,7,8,9,10 \ldots \ldots \)
The elements of the set are 1, 2, 3,4 and 5
The roaster form is
\(B=\{1,2,3,4,5\}\)
sets class 11 ncert solutions || class 11 ch 1 exercise solutions || sets class 11 ncert solutions || class 11 maths chapter 1 sets exercise 1.1 || ncert exemplar class 11 maths || class 11 chapter 1 exercise solution || ncert solution for class 11 maths chapter 1
3C. Write the following sets in roster form:
\( \mathrm{C}=\{x: x \) is a two-digit natural number such that the sum of its digits is \( 8\} \)
\( \mathrm{C}=\{x: x \) is a two-digit natural number such that the sum of its digits is \( 8\} \)
Answer
\( \text{The elements of the set are numbers} \ 17,26,35,44,53,62,71,80 \)
As \( 0+8=8 \) but putting 0 in tens place makes it single digit number so will not consider it.
\( 8+0=80 \), number is 80
\( 1+7=8 \), number is 17
\( 7+1=8 \), number is 71
\( 2+6=8 \), number is 26
\( 6+2=8 \), number is 62
\( 3+5=8 \), number is 35
\( 5+3=8 \), number is 53
\( 4+4=8 \), number is 44
Set in roaster form is
\(C=\{17,26,35,44,53,62,71,80\}\)
3D. Write the following sets in roster form:
\( \mathrm{D}=\{x: x \) is a prime number which is divisor of 60\( \} \)
\( \mathrm{D}=\{x: x \) is a prime number which is divisor of 60\( \} \)
Answer
Prime numbers are those which have factors as one and the number itself.
List of prime numbers is \( 2,3,5,7,11,13,17,19,21,23 \ldots \ldots \)
Divisors of 60 are \( 1,2,3,4,5,6,10,12,15,20,30,60 \)
So \( 1 \times 60=60 \)
\( 2 \times 30=60 \)
\( 3 \times 20=60 \)
\( 4 \times 15=60 \)
\( 5 \times 12=60 \)
\( 6 \times 10=60 \)
The elements of the set are prime numbers which are divisor of 60 that is 2,3 and 5 .
The roaster form of set is
\(\mathrm{D}=\{2,3,5\}\)
3E. Write the following sets in roster form:
\( \mathrm{E}= \) The set of all letters in the word TRIGONOMETRY
\( \mathrm{E}= \) The set of all letters in the word TRIGONOMETRY
Answer
There are 12 letters in the word TRIGONOMETRY out of which T, R and O are repeating
So the element of the set is T, R, I, G, O, N, M, E and Y
The set in the roaster form is
\(E=\{T, R, I, G, O, N, M, E, Y\}\)
3F. Write the following sets in roster form:
\( \mathrm{F}= \) The set of all letters in the word BETTER
\( \mathrm{F}= \) The set of all letters in the word BETTER
Answer
There are four letters in the word B, E, T, R. T and E are repeating in the word.
So the elements of the set are B, E, T, R.
The set in the roaster form is \( F=\{B, E, T, R\} \)
4A. Write the following sets in the set-builder form:
\( (3,6,9,12\} \)
\( (3,6,9,12\} \)
Answer
Here the element of the set can be disintegrated as
\(3=3 \times 1\)
\(6=3 \times 2\)
\(9=3 \times 3\)
\(12=3 \times 4\)
The set in the set-builder form is
\( \mathrm{A}=\{x: x=3 \mathrm{n} \) where \( \mathrm{n} \in \mathrm{N} \) and \( 1 \leq \mathrm{n} \leq 4\} \)
4B. Write the following sets in the set-builder form:
\(\{2,4,8,16,32\}\)
\(\{2,4,8,16,32\}\)
Answer
The elements of the set can be disintegrated as
\(2=2^{1}\)
\(4=2^{2}\)
\(8=2^{3}\)
\(16=2^{4}\)
\(32=2^{5}\)
The set in the set-builder form is
\(\mathrm{A}=\{x: x=2 \mathrm{n}, \mathrm{n} \in \mathrm{N} \text { and } 1 \leq \mathrm{n} \leq 5\}\)
sets class 11 ncert solutions || class 11 ch 1 exercise solutions || sets class 11 ncert solutions || class 11 maths chapter 1 sets exercise 1.1 || ncert exemplar class 11 maths || class 11 chapter 1 exercise solution || ncert solution for class 11 maths chapter 1
4C. Write the following sets in the set-builder form:
\(\{5,25,125,625\}\)
\(\{5,25,125,625\}\)
Answer
The elements of the set can be disintegrated as
\(5=5^{1}\)
\(25=5^{2}\)
\(125=5^{3}\)
\(625=5^{4}\)
The set in the set-builder form is
\( \mathrm{A}=\{x: x=5 \mathrm{n}, \mathrm{n} \in \mathrm{N} \) and \( 1 \leq \mathrm{n} \leq 4\} \)
4D. Write the following sets in the set-builder form:
\( \{2,4,6, \ldots\} \)
\( \{2,4,6, \ldots\} \)
Answer
Natural numbers are \( 1,2,3,4,5,6 \ldots \)
Even natural numbers are \( 2,4,6,8 \ldots \)
\( \therefore \) the given set is set of all even natural numbers
The set in the set-builder form is
\( A=\{x: x=2 k \) for unique value of \( k, k > 0\} \)
4E. Write the following sets in the set-builder form: \( \{1,4,9, \ldots, 100\} \)
Answer
The element of the set can be disintegrated as
\(1=1^{2}\)
\(4=2^{2}\)
\(9=3^{2}\)
\(\ldots\)
\(\ldots\)
\(\ldots\)
\(100=10^{2}\)
The set in the set-builder form i
\(\mathrm{A}=\{x: x=\mathrm{n} 2, \mathrm{n} \in \mathrm{N}, 1 \leq \mathrm{n} \leq 10\}\)
Alternatively
\( \mathrm{A}=\{x: x \) is the square of natural number less than or equal to 10\( \} \)
5A. List all the elements of the following sets:
\( \mathrm{A}=\{x: x \) is an odd natural number \( \} \)
\( \mathrm{A}=\{x: x \) is an odd natural number \( \} \)
Answer
Natural numbers are \( 1,2,3,4,5,6,7,8,9,10 \ldots \ldots \ldots \ldots \ldots\)
Odd natural numbers are \( 1,3,5,7,9,11, \ldots \ldots \ldots \ldots \ldots \)
So the elements of the set are \( 1,3,5,7,9,11 \ldots \ldots \ldots \ldots \ldots\)
\(A=\{1,3,5,7,9,11, \ldots\}\)
5B. List all the elements of the following sets:
\( B=\{x: x \) is an integer, \(-\frac{1 }{ 2 } < x < \frac{ 9 }{ 2 }\} \)
\( B=\{x: x \) is an integer, \(-\frac{1 }{ 2 } < x < \frac{ 9 }{ 2 }\} \)
Answer
Here, Given \( -\frac{ 1 }{ 2 } < x < \frac{ 9 }{ 2 }\} \)
\(\Rightarrow-0.5 < x < 4.5\)
Integers \( = \ldots\) \( -4,-3,-2,-1,0,1,2,3,4,5,6 \) \( \qquad \)
Elements of the given set are \( 0,1,2,3,4 \)
\(B=\{0,1,2,3,4\}\)
sets class 11 ncert solutions || class 11 ch 1 exercise solutions || sets class 11 ncert solutions || class 11 maths chapter 1 sets exercise 1.1 || ncert exemplar class 11 maths || class 11 chapter 1 exercise solution || ncert solution for class 11 maths chapter 1
5C. List all the elements of the following sets:
\( C=\{x: x \) is an integer, \( x 2 \leq 4\} \)
\( C=\{x: x \) is an integer, \( x 2 \leq 4\} \)
Answer
Integers are \( \ldots \ldots-4,-3,-2,-1,0,1,2,3,4,5,6,7,8 \)
\(x^{2}=4\)
\(x= \pm 2\)
\(\text { so }-2 \leq x \leq 2\)
\((0)^{2}=0\)
\((1)^{2}=1\)
\((2)^{2}=4\)
\((-2)^{2}=4\)
\((-1)^{2}=1\)
The elements of the set are \( -2,-1,0,1 \),
\(\mathrm{C}=\{-2,-1,0,1,2\}\)
5D. List all the elements of the following sets:
\(\mathrm{D}=\{x: x \text { is a letter in the word "LOYAL" }\}\)
\(\mathrm{D}=\{x: x \text { is a letter in the word "LOYAL" }\}\)
Answer
There are four letters in the word \( \mathrm{L}, \mathrm{O}, y, \mathrm{A} \) as L is repeating
The element of the sets is \( \mathrm{L}, \mathrm{O}, y, \mathrm{A} \)
\(\mathrm{D}=\{\mathrm{L}, \mathrm{O}, y, \mathrm{A}\}\)
5E. List all the elements of the following sets:
\( \mathrm{E}=\{x: x \) is a month of a year not having 31 days \( \} \)
\( \mathrm{E}=\{x: x \) is a month of a year not having 31 days \( \} \)
Answer
The set would include months with 30 days and 28 days (February)
Now the elements of the set would be months: - February, April, June, September and November
\( E=\{ \) February, April, June, September, November \( \} \)
5F. List all the elements of the following sets:
\( \mathrm{F}=\{x: x \) is a consonant in the English alphabet which precedes k\( \} \).
\( \mathrm{F}=\{x: x \) is a consonant in the English alphabet which precedes k\( \} \).
Answer
The vowels are a, e, i, o, u
The letters before k are \( \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}, \mathrm{i}, \mathrm{j}, \mathrm{k} \)
Thus the consonant before \( k \) are \( b, c, d, f, g, h, j \)
So, the elements of the sets are \( b, c, d, f, g, h, j \)
\( F=\{b, c, d, f, g, h, j\} \)
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:
\(\begin{array}{|l|l|}
\hline (i) \{1,2,3,6\} & \begin{array}{l}
A. \{x: x \ \text{is a prime number and a} \\
\text{divisor of} \ 6 \}
\end{array} \\
\hline (ii) \{2,3\} & \begin{array}{l}
B. \{x: x \ \text{is an odd natural less than} \\
10\}
\end{array} \\
\hline (iii) \{\mathrm{M}, \mathrm{A}, \mathrm{T}, \mathrm{H}, \mathrm{E}, \mathrm{I}, \mathrm{C}, \mathrm{S}\} & \begin{array}{l}
C. \{x: x \ \text{is natural number and} \\
\text{divisor of 6} \}
\end{array} \\
\hline (iv) \{1,3,5,7,9\} & \begin{array}{l}
D. \{x: x \ \text{is a letter of the word} \\
\text{MATHEMATICS} \}
\end{array} \\
\hline
\end{array}\)
\(\begin{array}{|l|l|}
\hline (i) \{1,2,3,6\} & \begin{array}{l}
A. \{x: x \ \text{is a prime number and a} \\
\text{divisor of} \ 6 \}
\end{array} \\
\hline (ii) \{2,3\} & \begin{array}{l}
B. \{x: x \ \text{is an odd natural less than} \\
10\}
\end{array} \\
\hline (iii) \{\mathrm{M}, \mathrm{A}, \mathrm{T}, \mathrm{H}, \mathrm{E}, \mathrm{I}, \mathrm{C}, \mathrm{S}\} & \begin{array}{l}
C. \{x: x \ \text{is natural number and} \\
\text{divisor of 6} \}
\end{array} \\
\hline (iv) \{1,3,5,7,9\} & \begin{array}{l}
D. \{x: x \ \text{is a letter of the word} \\
\text{MATHEMATICS} \}
\end{array} \\
\hline
\end{array}\)
Answer
\(\begin{array}{|l|l|}
\hline (i) \{1,2,3,6\} & \begin{array}{l}
C. \{x: x \ \text{is natural number and} \\
\text{divisor of 6} \}
\end{array} \\
\hline
\end{array}\)
The elements of sets are
\(\begin{array}{l}
6 \times 1=6 \\
3 \times 2=6
\end{array}\)
\( \{1,2,3,6\} \) is a set of natural numbers and divisor of 6
(ii) \(\begin{array}{|l|l|}
\hline \{2,3\} & \begin{array}{l}
A. \{x: x \text{ is a prime number and a} \\
\text{divisor of 6} \}
\end{array} \\
\hline
\end{array} \)
\(6 \times 1=6\)
\(2 \times 3=6\)
The divisors of 6 are 1, 6, 2 and 3 out of which 2 and 3 are prime \( \{2,3\} \) is the set of prime numbers which are divisor of 6
\(\begin{array}{|l|l|}
\hline (iii) \{\mathrm{M}, \mathrm{A}, \mathrm{T}, \mathrm{H}, \mathrm{E}, \mathrm{I}, \mathrm{C}, \mathrm{S}\} & \begin{array}{l}
D. \{x: x \ \text{is a letter of the word} \\
\text{MATHEMATICS} \}
\end{array} \\
\hline
\end{array} \)
There are 11 letters in the word MATHEMATICS out of which 3 (M, T, A) are repeating.
\( \{\mathrm{M}, \mathrm{A}, \mathrm{T}, \mathrm{H}, \mathrm{E}, \mathrm{I}, \mathrm{C}, \mathrm{S}\} \) is a set of letters of the word MATHEMATICS \(\begin{array}{|l|l|}
\hline (iv) \{1,3,5,7,9\} & \begin{array}{l}
B. \{x: x \ \text{is an odd natural less than} \\
10\}
\end{array} \\
\hline
\end{array} \)
Natural numbers are \( 1,2,3,4,5,6,7,8,9 \),
Odd numbers less than 10 are \( 1,3,5,7,9 \)
\( \{1,3,5,7,9\} \) is a set of odd natural numbers less than 10
