Exercise 1.1 NCERT Class 11 Chapter 1 Sets contains 6 questions. All questions of this exercise have been fully solved. You can excess them from the links given below.
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Exercise 1.1 NCERT Class 11 Math Solutions
The first question of Exercise 1.1 NCERT Class 11 is related to the definition of sets.
1. Which of the following are sets? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
Answer
The set of collection of all the months of a year beginning with the letter J is
A is a set as we can clearly specify which elements belong to A and which do not.
We can say that the names of months starting with the letter 'J' are only January, June, and July and not February, March, April, May, August, September, October, November, and December.
(ii) The collection of ten most talented writers of India.
Answer
The collection of the ten most talented writers of India is not a set, as we cannot clearly specify which writer is most talented and which is not.
A writer may be most talented in fiction and may be bad in non-fiction. So, we will be unable to find the most talented writer in India.
(iii) A team of eleven best-cricket batsmen of the world.
Answer
A team of the eleven best cricket batsmen in the world is not a set, as we cannot form a team which is the best cricket team in the world. We cannot say clearly that a cricket team is the best in the world.
(iv) The collection of all boys in your class.
Answer
The collection of all boys in your class is clearly a set, as we can clearly specify whether a boy studies in your class or not.
(v) The collection of all natural numbers less than 100.
Answer
The collection of all natural numbers less than 100 is a set, as we can clearly specify whether a natural number is less than 100 or not.
(vi) The collection of novels written by Munshi Prem Chand.
Answer
The collection of novels written by Munshi Prem Chand is a set, as it is possible to list all the novels written by Munshi Prem Chand.
We can clearly specify whether a novel is written by Munshi Prem Chand or not.
(vii) The collection of all even integers.
Answer
The collection of all even integers is a set, as we can clearly specify whether an integer is even or not.
(viii) The collection of questions in this Chapter.
Answer
The collection of questions in this chapter is a set, as we can clearly specify whether a question is a question of this chapter or not.
(ix) The collection of most dangerous animals of the world.
Answer
The collection of the most dangerous animals in the world is not a set, as we cannot clearly specify which animals are the most dangerous and which are not.
The second question of Exercise 1.1 NCERT Class 11 is related to inserting relevant symbol of sets in blank spaces.
2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol or in the blank spaces:
(i) 5 . . . A
Answer
5 is a member of the set A = {1, 2, 3, 4, 5, 6}
5 ∈ A.
(ii) 8 . . . A
Answer
8 is not a member of the set A = {1, 2, 3, 4, 5, 6}
8 ∉ A.
(iii) 0 . . . A
Answer
0 is not a member of the set A = {1, 2, 3, 4, 5, 6}
0 ∉ A.
(iv) 4 . . . A
Answer
4 is a member of the set A = {1, 2, 3, 4, 5, 6}
4 ∈ A.
(v) 2 . . . A
Answer
2 is a member of the set A = {1, 2, 3, 4, 5, 6}
2 ∈ A.
(vi) 10 . . . A
Answer
10 is not a member of the set A = {1, 2, 3, 4, 5, 6}
5 ∉ A.
The third question of Exercise 1.1 NCERT Class 11 is related to the roster form of sets.
3. Write the following sets in roster form:
(i) A = {x : x is an integer and
Answer
A = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = {x : x is a natural number less than 6}
Answer
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}
Answer
C = {17, 71, 26, 62, 35, 53, 44, 80} Here, sum of digits of the numbers in the set is 8.
(iv) D = {x : x is a prime number which is divisor of 60}
Answer
D = {2, 3, 5}
(v) E = The set of all letters in word TRIGONOMETRY
Answer
E = {T, R, I, G, O, N, M, E, Y} We should not repeat the same letters again, as the same number is not counted as a different member in a set.
(vi) F = The set of all letters in the word BETTER
Answer
F = {B, E, T, R}
The fourth question of Exercise 1.1 NCERT Class 11 is related to the set-builder form of sets.
4. Write the following sets in the set-builder form:
(i) {3, 6, 9, 12}
Answer
Here, every element of the set is a multiple of 3. So, we can represent every number as product of 3 and a variable which varies from 1 to 4. Hence the set-builder form is {x : x = 3n, n∈N, and }
(ii) {2, 4, 8, 16, 32}
Answer
Here, every number is some power of 2. So, its set-builder form is
{x : x = 2n, n∈N and }
(iii) {5, 25, 125, 625}
Answer
Here, every element is formed by raising some power of 5.
We can write , , , . Now, we can generalise elements by supposing , where n varies from 1 to 4.
So, we can write the given set in set builder form as follows:
{x : x = 5n, n∈N and }
(iv) {2, 4, 6, . . .}
Answer
Here, every element of the given set is an even natural number. Since the given set is an infinite set, we can just write the property of each number.
We can write the set-builder form of the set in two ways:
{x : x is an even natural number}
or
{x : x = 2n, n∈N, n = 1, 2, 3, . . . }
(v) {1, 4, 9, . . . , 100}
Answer
Here, each element is the square of a natural number. For example, 1 = 12, 4 = 22, 9 = 32, . . . , 100 = 102.
So, we can write the set-builder form of the set as follows:
{x : x = n2, n∈N and }
The fifth question of Exercise 1.1 NCERT Class 11 is related to the definition of sets.
5. List all the elements of the following sets:
(i) A = {x : x is an odd natural number}
Answer
The elements of the given set A are odd natural numbers i.e. 1, 3, 5, . . .
So, the set representing list of elements is
A = {1, 3, 5, 7, 9, . . . ∞}
(ii) B = {x : x is an integer, }
Answer
Here, x is an integer between and . Hence, the set representing list of elements is given as follows:
B = {0, 1, 2, 3, 4}
(iii) C = {x : x is an integer, }
Answer
Here, we have,
But is an integer, so the list of integers in the set [-2, 2] are :
C = {-2, -1, 0, 1, 2}
(iv) D = {x : x is a letter in the word "LOYAL"}
Answer
Clearly, the list of letters in the word "LOYAL" is given as follows:
D = {L, O, Y, A}
(v) E = {x : x is a month of a year not having 31 days}
Answer
We know that
Number of days in the month of January = 31
Number of days in the month of February = 28 or 29
Number of days in the month of March = 31
Number of days in the month of April = 30
Number of days in the month of May = 31
Number of days in the month of June = 30
Number of days in the month of July = 31
Number of days in the month of August = 31
Number of days in the month of September = 30
Number of days in the month of October = 31
Number of days in the month of November = 30
Number of days in the month of December = 31
Clearly, the set representing the list of months not having 31 days is:
E = {February, April, June, September, November}
(v) F = {x : x is a consonant in the English alphabet which precedes k}
Answer
2 is a member of the set A = {1, 2, 3, 4, 5, 6}
2 ∈ A.
The sixth question of Exercise 1.1 NCERT Class 11 is about matching the roster form of set with its set-builder form of the set.
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 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 natural number and divisor of 6} |
| (iv) {1, 3, 5, 7, 9} | (d) {x : x is a letter of the word MATHEMATICS} |
Answer
| (i) {1, 2, 3, 6} | (c) {x : x is natural number and divisor of 6} |
| (ii) {2, 3} | (a) {x : x is a prime number and a divisor of 6} |
| (iii) {M, A, T, H, E, I , C, S} | (d) {x : x is a letter of the word MATHEMATICS} |
| (iv) {1, 3, 5, 7, 9} | (b) {x : x is an odd natural number less than 10} |
