Class-11 NCERT Solution Chapter-1 SETS Exercise 1.1

EXERCISE 1.1

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.

Ans: The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identify a month that belongs to this collection ie January, June, July are the only 3 months beginning with letter J. Hence, this collection is a set.

(ii) The collection of ten most talented writers of India.

Ans: The collection of ten most talented writers of India is not a well-defined collection because the criteria for determining a writer’s talent may vary from one person to other. Hence, this collection is not a set.

(iii) A team of eleven best-cricket batsmen of the world.

Ans: A team of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for determining a batsman’s talent may vary from one person to other. Hence, this collection is not a set.

(iv) The collection of all boys in your class.

Ans: The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection. Hence, this collection is a set.

(v) The collection of all natural numbers less than 100.

Ans: The collection of all natural numbers less than 100 is a well-defined collection because one can definitely identify a number that belongs to this collection. Hence, this collection is a set.

(vi) A collection of novels written by the writer Munshi Prem Chand.

Ans: A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because one can definitely identify a book that belongs to this collection. Hence, this collection is a set.

(vii) The collection of all even integers.

Ans: The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection. Hence, this collection is a set.

(viii) The collection of questions in this Chapter.

Ans: The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter. Hence, this collection is a set.

(ix) A collection of most dangerous animals of the world.

Ans: The 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 one person to other. Hence, this collection is not a set.

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

Reason: As 5,4,2 is a member of set A hence we use symbol ∈

Whereas 8,0,10 is not a member of set A hence we use symbol ∉

3. Write the following sets in roster form:

(i) A = {x : x is an integer and –3 ≤ x < 7}

Ans: The elements of this set are –3,–2, –1, 0, 1, 2, 3, 4, 5, and 6 only. Therefore, the given set can be written in roster form as

A = {–3,–2, –1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {x : x is a natural number less than 6}

Ans: The elements of this set are 1, 2, 3, 4, and 5 only. Therefore, the given set can be written in roster form as

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}

Ans: The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only. Therefore, this set can be written in roster form as

C = {17, 26, 35, 44, 53, 62, 71, 80}

(iv) D = {x : x is a prime number which is divisor of 60}

Ans: 60 = 2 × 2 × 3 × 5 The elements of this set are 2, 3, and 5 only. Therefore, this set can be written in roster form as

D = {2, 3, 5}.

(v) E = The set of all letters in the word TRIGONOMETRY

Ans: There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated, that’s why we consider them only one time. Therefore, this set can be written in roster form as

E = {T, R, I, G, O, N, M, E, Y}

(vi) F = The set of all letters in the word BETTER

Ans: There are 6 letters in the word BETTER, out of which letters E and T are repeated, that’s why we consider them only once. Therefore, this set can be written in roster form as    F = {B, E, T, R}

4. Write the following sets in the set-builder form :

(i) (3, 6, 9, 12}

Ans: We can observe that this set contains multiple of 3 from 3 to 12 ie (3X1), (3X2), (3X3), (3X4). Hence in set builder form we can write it as

{x: x = 3n, n∈ N and 1 ≤ n ≤ 4}

(ii) {2,4,8,16,32}

Ans: It can be seen that (2 = 2¹), (4 = 2²), (8 =2³), (16 =2⁴), and (32 =2⁵).

∴ {2, 4, 8, 16, 32} = {x: x = 2ⁿ, n∈ N and 1 ≤ n ≤ 5}

(iii) {5, 25, 125, 625}

Ans: {5, 25, 125, 625} It can be seen that (5 = 5¹), (25 =5²), (125 =5³), and (625 =5⁴).

∴ {5, 25, 125, 625} = {x: x = 5ⁿ, n ∈ N and 1 ≤ n ≤ 4}

(iv) {2, 4, 6, . . .}

Ans: {2, 4, 6 …} It is a set of all even natural numbers.

∴ {2, 4, 6 …} = {x: x is an even natural number}

(v) {1,4,9, . . .,100}

Ans: {1, 4, 9 … 100} It can be seen that (1 =1²), (4 =2²), (9 =3²), …(100 =10²)

 ∴ {1, 4, 9… 100} = {x: x = n², n ∈ N and 1 ≤ n ≤ 10}

5. List all the elements of the following sets :

(i) A = {x : x is an odd natural number}

Ans: All elements of this set are   1, 3, 5, 7, 9 …

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

Ans: Solving the fraction we get (–1/2  = -0.5)    and    (9/2 = 4.5)

      All elements of this set are    0,1,2,3,4

(iii) C = {x : x is an integer, x²≤ 4}

Ans: It can be seen that

(–1)² = 1 ≤ 4;                         (–2)² = 4 ≤ 4;                      (–3)² = 9 > 4

0² = 0 ≤ 4                                                        1² = 1 ≤ 4

2² = 4 ≤ 4                                                        3² = 9 > 4

 ∴ All elements of this set are  –2, –1, 0, 1, 2

(iv) D = {x : x is a letter in the word “LOYAL”}

 Ans:  All elements of this set are     L, O, Y, A

(v) E = {x : x is a month of a year not having 31 days}

Ans:  All elements of this set are      February, April, June, September, November

(vi) F = {x : x is a consonant in the English alphabet which precedes k }

Ans:  All elements of this set are    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:

(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}.

i. All the elements of this set are natural numbers as well as the divisors of 6. Therefore, (i) matches with (c).

ii. It can be seen that 2 and 3 are prime numbers. They are also the divisors of 6. Therefore, (ii) matches with (a).

iii. All the elements of this set are letters of the word MATHEMATICS. Therefore, (iii) matches with (d).

iv. All the elements of this set are odd natural numbers less than 10. Therefore, (iv) matches with (b).

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