NCERT Solutions for Exercise 1.1, Class 11, Maths

Exercise 1.1 Sets
Question and Answers
Class 11 – Maths

Class	Class 11
Subject	Mathematics
Chapter Name	Sets
Chapter No.	Chapter 1
Exercise	Exercise 1.1
Category	Class 11 Maths NCERT Solutions

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 

(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 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 any 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 most dangerous animals of 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.

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}

–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}

The divisors of 60 are 2,3,4,5,6. Among these, the prime numbers are 2, 3, 5

The elements of the set are 2 , 3 , 5

∴The roaster form of the set D={ x:x is a prime number which is divisor of 60 } is 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 roster 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}

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}

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}.

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, – 1/ 2  < x < 9/ 2 }

(iii) C = {x : x is an integer, x ² ≤ 4}

(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 precedes k }.

Answer 

(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}

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) {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}