Written by : Anmol Gupta
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NCERT Class 11 Maths Chapter 1 SETS Exercise 1.1 Solutions
Table of Contents
Solved Examples before Exercise 1.1
Example 1. Write the solution set of the equation x2 + x – 2 = 0 in roster form.
Answer 1.
x2 + x – 2 = 0
x2 + 2x – x – 2 = 0
x(x+2) – (x+2) = 0
(x – 1) (x + 2) = 0, i. e., x = 1, – 2
Therefore, the solution set of the given equation can be written in roster form as {1, – 2}
Example 2. Write the set {x : x is a positive integer and x2< 40} in the roster form
Answer 2.
Zero is neither positive nor negative, so we start with number 1
1 is a positive integer, 12 < 40
2 is a positive integer, 22 < 40
3 is a positive integer, 32 < 40
4 is a positive integer, 42 < 40
5 is a positive integer, 52 < 40
6 is a positive integer, 62 < 40
7 is a positive integer but 72 > 40 so we stop till above
So, the given set in the roster form is {1, 2, 3, 4, 5, 6}
Example 3. Write the set A = {1, 4, 9, 16, 25, . . . } in set-builder form.
Answer 3.
We can write A = { 12, 22, 32, 42, 52 ,…}
Means A = {x : x is the square of a natural number}
Alternatively, we can write A = {x : x = n2, where n ∈ N}
Example 4. Write the set 
in the set builder form
Answer 4.
The set can be written as
{ x : x = 
, where n is a natural number and 1≤n≤6 }
Example 5. Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form :
Answer 5.
(i) matches with (d) since in (d), there are 9 letters in the word PRINCIPAL and two letters P and I are repeated
(ii) matches (c) as x + 1 = 1 implies x = 0
(iii) matches (a) as 1, 2 ,3, 6, 9, 18 are all divisors or factors of 18
(iv) matches (b) as
x2 – 9 = 0
x2 – 32 = 0
(x+3)(x-3) = 0
x=3 and x = -3
Exercise 1.1 solved questions
Question 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.
(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.
Answer 1.
(i) Yes as the collection is well defined
(ii) No as the collection of ten most talented writers of India may differ from one person to another and thus is not well defined
(iii) No as the collection of team of eleven best-cricket batsmen of the world may differ from one person to another and thus is not well defined
(iv) Yes as the collection is well defined
(v) Yes as the collection is well defined
(vi) Yes as the collection is well defined
(vii) Yes as the collection is well defined
(viii) Yes as the collection is well defined
(ix) No, as the collection of most dangerous animals of the world may may differ from one person to another and thus is not well defined
Question 2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces:
(i) 5. . .A (ii) 8 . . . A (iii) 0. . .A
(iv) 4. . . A (v) 2. . .A (vi) 10. . .A
Answer 2.
(i) 5 ∈ A (ii) 8 ∉ A (iii) 0∉ A
(iv) 4 ∈ A (v) 2 ∈ A (vi) 10 ∉ A
Question 3. Write the following sets in roster form:
(i) A = {x : x is an integer and –3 ≤ x < 7}
(ii) B = {x : x is a natural number less than 6}
(iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x : x 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
Answer 3.
(i) A = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = { 1, 2, 3, 4, 5 }
(iii) In 2 digit natural numbers 17, 26, 35, 44, 53, 62, 71, 80 sum of their digits add to 8
C = { 17, 26, 35, 44, 53, 62, 71, 80 }
(iv) Divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Among them, prime numbers are 2, 3, 5.
In roster form, D = {2, 3, 5}
(v) In the word TRIGONOMETRY, letters T, R, O are repeated, excluding the repetitions
E = { T, R, I, G, O, N, M, E, Y }
(vi) In the word BETTER, letters E and T are repeated, excluding the repetitions
F = { B, E, T, R }
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}
Answer 4.
(i) It can be written as 3 × 1, 3 × 2, 3 × 3, 3 × 4
Means 3n where n is a natural number and 1≤n≤4
{3, 6, 9 ,12} = {x : x = 3n, n ∈ N and 1≤n≤4}
(ii) It can be written as 21, 22, 23, 24, 25
Means 2n , where n is a natural number and 1≤n≤5
{2, 4, 8, 16, 32} = { x : x =2n , n ∈ N and 1≤n≤5 }
(iii) It can be written as 51, 52, 53, 54
Means 5n , where n is a natural number and 1≤n≤4
{5, 25, 125, 625} = { x : x = 5n , n ∈ N and 1≤n≤4 }
(iv) It can be written as 2 × 1, 2 × 2, 2 × 3, 2 × 4….
Means 2n, where n is a natural number
{2, 4, 6, . . .} = { x : x = 2n, n ∈ N }
(v) It can be written as 12 , 22 , 32 ,…..102
Means n2 where n is a natural number and 1≤n≤10
{1,4,9, . . .,100} = { x : x = n2 , n ∈ N and 1≤n≤10 }
Question 5. List all the elements of the following sets :
Answer 5.
(i) A = { 1, 3, 5, 7, 9 }
(ii) B = { 0, 1, 2, 3, 4 }
(iii) (-3)2 = 9
(-2)2 = 4
(-1)2 = 1
(0)2 = 0
(1)2 = 1
(2)2 = 4
(3)2 = 9
So, B = { -2, -1, 0, 1, 2 }
(iv) As L is repeating 2 times, we write it one time
D = { L, O, Y, A }
(v) E = { February, April, June, September, November }
(vi) Consonants are any of the letters of the English alphabet except vowels, that is, except, a, e, i, o, and u
F = { b, c, d, f, g, h, j }
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:
Answer 6.
(i) matches with (c) as 1, 2, 3, 6 are natural numbers and are divisors of 6
(ii) matches (a) as 2, 3 are prime numbers and also divisors of 6
(iii) matches (d) as MATHEMATICS can be written in roster form as {M, A, T, H, E, I, C, S}
(iv) matches (b) as 1, 3, 5, 7, 9 are odd natural numbers and less than 10
