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} |
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