# Sets Exercise 1.1 Solutions – NCERT Class 11 Mathematics Chapter 1

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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
The collection of all months of a year beginning with letter J is January, June, July which is a well defined collection of objects(words) that’s why it will be a Set.

(ii) The collection of ten most talented writers of India
Collection of Ten Most Talented writers of India is not a certain list, as everybody in India can be fan of different writers which means if asked to every Indian the list of Most Ten Talented writers would be different for each one of Indian. This means that collection of ten most talented writers of India is not a well defined collection hence it’s not a Set.

(iii) A team of eleven best-cricket batsmen of the world
What makes a batsmen best is not well defined, so if asked to people from different countries they will come up with different teams which they think contain eleven best-cricket batsmen of the world. As team of eleven best-cricket batsmen of the world is not well defined and depends upon personal choices of people. That’s why it’s not a Set.

(iv) The collection of all boys in your class
Collection of all boys in a class is well defined that’s why it’s a Set.

(v) The collection of all natural numbers less than 100
All natural numbers which are less than 100 are 1, 2, 3, 4, 5 ………. 99 which is a well defined list of numbers. That’s why collection of all natural numbers less than 100 is a Set.

(vi) A collection of novels written by the writer Munshi Prem Chand
Collection of novels written by the writer Munshi Prem Chand is a well defined list. That’s why its a Set.
One thing to note here is that statement “A collection of novels written by Munshi Prem Chand” is not a Set because this sentence clearly does not state which Munshi Prem Chand. Is it famous Munshi Prem Chand or some common person whose name is Munshi Prem Chand. So statement “A collection of novels written by Munshi Prem Chand” is not well defined hence it will not be a Set.

A collection of novels written by the writer Munshi Prem Chand – is a Set
A collection of novels written by Munshi Prem Chand – is not a Set

(vii) The collection of all even integers
The collection of all even integers is 2, 4, 6, 8, 10, 12, ……………. which is well defined hence it’s a Set

(viii) The collection of questions in this Chapter
Collection of questions in a chapter is well defined that’s why it’s a Set

(ix) A collection of most dangerous animals of the world
Collection of most dangerous animals of the world is not well defined, that’s why it’s not a Set

2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces:
(i) 5. . .A
As 5 is in Set A = {1, 2, 3, 4, 5, 6} that’s 5 ∈ A

(ii) 8 . . . A
As 8 is not in Set A = {1, 2, 3, 4, 5, 6} that’s 5 ∉ A

(iii) 0. . .A
As 0 is not in Set A = {1, 2, 3, 4, 5, 6} that’s 0 ∉ A

(iv) 4. . . A
As 4 is in Set A = {1, 2, 3, 4, 5, 6} that’s 4 ∈ A

(v) 2. . .A
As 2 is in Set A = {1, 2, 3, 4, 5, 6} that’s 2 ∈ A

(vi) 10. . .A
As 10 is not in Set A = {1, 2, 3, 4, 5, 6} that’s 10 ∉ A

3. Write the following sets in roster form:
(i) A = {x : x is an integer and –3 ≤ x < 7}
Set A contains x such that x is an integer and it lies between -3 and 7 (-3 included but 7 excluded).
Hence A = {-3 , -2, -1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {x : x is a natural number less than 6}
Set B contains x such that x is a natural number less than 6
Hence 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}
Set C contains x such that x is a two-digit natural number such that the sum of its digits is 8
Hence C = {17, 26, 35, 44, 53, 62, 71}

(iv) D = {x : x is a prime number which is divisor of 60}
Set D contains x such that x is a prime number which is divisor of 60
Hence D = {2, 3, 5}

(v) E = The set of all letters in the word TRIGONOMETRY
There are some repeated letters in word TRIGONOMETRY but upon forming a set only unique letters should be included.
Hence E = {T, R, I, G, O, N, M, E, Y}

(vi) F = The set of all letters in the word BETTER
There are some repeated letters in word BETTER but upon forming a set only unique letters should be included.
Hecen F = {B, E, T, R}

4. Write the following sets in the set-builder form
(i) {3, 6, 9, 12}
So common thing amongst 3, 6, 9, 12 is that all of these are multiples of 3 but less than 15
Hence {3, 6, 9, 12} in Set Builder Form is {x | x is a natural number multiple of 3 and x < 15}

(ii) {2,4,8,16,32}
So common thing amongst 2, 4, 6, 8, 16, 32 is that all of these are powers of 2 but less than and equal to 32 which is 25
Hence {2, 4, 6, 8, 16, 32} in Set Builder Form is {x | x = 2n where n ∈ N and n ≤ 5}

(iii) {5, 25, 125, 625}
So common thing amongst 5, 25, 125, 625 is that all of these are powers of 5 but less than and equal to 625 which is 54
Hence {5, 25, 125, 625} in Set Builder Form is {x | 5n where n ∈ N and n ≤ 4}

(iv) {2, 4, 6, . . .}
So common thing amongst 2, 4, 6, ……. is that all of these numbers are multiples of 2 and even it’s a set of even number.
Hence {2, 4, 6, …. } in Set Builder Form is {x | x is an even natural numbers}

(v) {1,4,9, . . .,100}
So common thing amongst 1, 4, 9, ….. , 100 is that all of these numbers are squares of natural numbers up till square of 10.
Hence {1, 4, 9, …, 100} in Set Builder Form is {x | x = n2 where n ∈ N and n ≤ 10}

5. List all the elements of the following sets:
(i) A = {x : x is an odd natural number}

x is an odd natural number means {1, 3, 5, 7, 9, …….}

(ii) B = {x : x is an integer, – 1/2 < x < 9/2 }
x is an integer – 1/2 < x < 9/2 means {0, 1, 2, 3, 4}

(iii) C = {x : x is an integer, x2 ≤ 4}
x is an integer x2 ≤ 4 means {-2, -1, 0, 1, 2}

(iv) D = {x : x is a letter in the word “LOYAL”}
x is a letter in the word “LOYAL” means {L, O, Y, A}

(v) E = {x : x is a month of a year not having 31 days}
x is a month of a year not having 31 days means {February, April, June, September, November}

(vi) F = {x : x is a consonant in the English alphabet which precedes k}
x is a consonant in the English alphabet which preceded k means {b, e, 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:

(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}