Chapter 1: Sets Exercise 1.1

(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects, as one can identify a month which belongs to this collection.

Therefore, this collection is a set.

(ii) The collection of the ten most talented writers of India is not a well-defined collection, as the criteria to determine a writer’s talent may differ from one person to another.

Therefore, this collection is not a set.

(iii) A team of eleven best-cricket batsmen of the world is not a well-defined collection, as the criteria to determine a batsman’s talent may vary from one person to another.

Therefore, this collection is not a set.

(iv) The collection of all boys in your class is a well-defined collection, as you can identify a boy who belongs to this collection.

Therefore, this collection is a set.

(v) The collection of all natural numbers less than 100 is a well-defined collection, as one can find a number which belongs to this collection.

Therefore, this collection is a set.

(vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined collection, as one can find a book which belongs to this collection.

Therefore, this collection is a set.

(vii) The collection of all even integers is a well-defined collection, as one can find an integer which belongs to this collection.

Therefore, this collection is a set.

(viii) The collection of questions in this Chapter is a well-defined collection, as one can find a question which belongs to this chapter.

Therefore, this collection is a set.

(ix) A collection of the most dangerous animals in the world is not a well-defined collection, as the criteria to find the dangerousness of an animal can differ from one animal to another.

Therefore, this collection is not a set.

(i) 5 ∈ A

(ii) 8 ∉ A

(iii) 0 ∉ A

(iv) 4 ∈ A

(v) 2 ∈ A

(vi) 10 ∉ A

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

–2, –1, 0, 1, 2, 3, 4, 5, and 6 only are the elements of this set.

Hence, the given set can be written in roster form as

A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}

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

1, 2, 3, 4, and 5 only are the elements of this set.

Hence, 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}

17, 26, 35, 44, 53, 62, 71, and 80 only are the elements of this set.

Hence, the given 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}

Here, 60 = 2 × 2 × 3 × 5

2, 3 and 5 only are the elements of this set.

Hence, the given set can be written in roster form as

D = {2, 3, 5}

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

TRIGONOMETRY is a 12 letters word out of which T, R and O are repeated.

Hence, the given set can be written in roaster form as

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

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

BETTER is a 6 letters word out of which E and T are repeated.

Hence, the given set can be written in roster form as

F = {B, E, T, R}

(i) {3, 6, 9, 12}

The given set can be written in the set-builder form as {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}.

(ii) {2, 4, 8, 16, 32}

We know that 2 = 2¹, 4 = 2², 8 = 2³, 16 = 2⁴, and 32 = 2⁵.

Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as {x: x = 2ⁿ, n ∈ N and 1 ≤ n ≤ 5}.

(iii) {5, 25, 125, 625}

We know that 5 = 5¹, 25 = 5², 125 = 5³, and 625 = 5⁴.

Therefore, the given set {5, 25, 125, 625} can be written in the set-builder form as {x: x = 5ⁿ, n ∈N and 1 ≤ n ≤ 4}.

(iv) {2, 4, 6 …}

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

Therefore, the given set {2, 4, 6 …} can be written in the set-builder form as {x: x is an even natural number}.

(v) {1, 4, 9 … 100}

We know that 1 = 1², 4 = 2², 9 = 3² …100 = 10².

Therefore, the given set {1, 4, 9… 100} can be written in the set-builder form as {x: x = n², n ∈ N and 1 ≤ n ≤ 10}.

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

So, the elements are A = {1, 3, 5, 7, 9 …..}.

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

We know that – 1/2 = – 0.5 and 9/2 = 4.5

So, the elements are B = {0, 1, 2, 3, 4}.

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

We know that

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

Here,

0² = 0 ≤ 4, 1² = 1 ≤ 4, 2² = 4 ≤ 4, 3² = 9 > 4

So, we get

C = {–2, –1, 0, 1, 2}

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

So, the elements are D = {L, O, Y, A}

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

So, the elements are E = {February, April, June, September, November}

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

So, the elements are F = {b, c, d, f, g, h, j}

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

(ii) 2 and 3 are prime numbers which are divisors of 6. Hence, (ii) matches with (a).

(iii) The elements are the letters of the word MATHEMATICS. Hence, (iii) matches with (d).

(iv) The elements are odd natural numbers which are less than 10. Hence, (v) matches with (b).

The other exercise of Chapter 1 NCERT Class 11 Maths Solutions is as follows.

Exercise 1.2 Solutions 6 Questions

Exercise 1.3 Solutions 9 Questions

Exercise 1.4 Solutions 12 Questions

Exercise 1.5 Solutions 7 Questions

Exercise 1.6 Solutions 8 Questions

Miscellaneous Exercise on Chapter 1 Solutions 16 Questions