## NCERT Solutions for Class 11 Maths Chapter 1 – Sets Ex 1.1

#### Page No 4:

#### Question 1:

Which of the following are sets? Justify our answer.

**(i)**The collection of all 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:

**(i)**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.

Hence, this collection is a set.

**(ii)**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 person to person.

Hence, this collection is not a set.

**(iii)**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 person to person.

Hence, this collection is not a set.

**(iv)**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 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 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 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 is a well-defined collection because one can definitely identify a question that belongs to this chapter.

Hence, this collection is a set.

**(ix)**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 can vary from person to person.

Hence, this collection is not a set.

#### Page No 5:

#### 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:

**(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:

**(i)**A = {

*x*:

*x*is an integer and –3 <

*x*< 7}

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

Therefore, 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}

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}

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 a divisor of 60}

2 60 2 30 3 15 5

∴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

There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated.

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

There are 6 letters in the word BETTER, out of which letters E and T are repeated.

Therefore, this set can be written in roster form as

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:

**(i)**{3, 6, 9, 12} = {

*x*:

*x*= 3

*n*,

*n*∈ N and 1 ≤

*n*≤ 4}

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

It can be seen that 2 = 2

^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}, and 32 = 2^{5}.
∴ {2, 4, 8, 16, 32} = {

*x*:*x*= 2^{n},*n*∈ N and 1 ≤*n*≤ 5}**(iii)**{5, 25, 125, 625}

It can be seen that 5 = 5

^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}.
∴ {5, 25, 125, 625} = {

*x*:*x*= 5^{n},*n*∈N and 1 ≤*n*≤ 4}**(iv)**{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}

It can be seen that 1 = 1

^{2}, 4 = 2^{2}, 9 = 3^{2}…100 = 10^{2}.
∴ {1, 4, 9… 100} = {

*x*:*x*=*n*^{2},*n*∈N and 1 ≤*n*≤ 10}#### Question 5:

List all the elements of the following sets:

**(i)**A = {

*x*:

*x*is an odd natural number}

**(ii)**B = {

*x*:

*x*is an integer,}

**(iii)**C = {

*x*:

*x*is an integer,}

**(iv)**D = {

*x*:

*x*is a letter in the word “LOYAL”}

**(v)**E = {

*x*:

*x*is a month of a year not having 31 days}

**(vi)**F = {

*x*:

*x*is a consonant in the English alphabet which proceeds

*k*}.

#### Answer:

**(i)**A = {

*x*:

*x*is an odd natural number} = {1, 3, 5, 7, 9 …}

**(ii)**B = {

*x*:

*x*is an integer;}

It can be seen that and

∴ B

**(iii)**C = {

*x*:

*x*is an integer;}

It can be seen that

(–1)

^{2}= 1 ≤ 4; (–2)^{2}= 4 ≤ 4; (–3)^{2}= 9 > 4
0

^{2}= 0 ≤ 4
1

^{2}= 1 ≤ 4
2

^{2}= 4 ≤ 4
3

^{2}= 9 > 4
∴C = {–2, –1, 0, 1, 2}

**(iv)**D = (

*x*:

*x*is a letter in the word “LOYAL”) = {L, O, Y, A}

**(v)**E = {

*x*:

*x*is a month of a year not having 31 days}

= {February, April, June, September, November}

**(vi)**F = {

*x*:

*x*is a consonant in the English alphabet which precedes

*k*}

= {

*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:

(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)**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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