NCERT Solutions Class 11 Maths Chapter 1 Set – Ex 1.1

NCERT Solutions Class 11 Maths 

The NCERT Solutions in English Language for Class 11 Mathematics Chapter – 1 Sets Exercise 1.1 has been provided here to help the students in solving the questions from this exercise. 

Chapter 1 (Sets) 

Chapter : 1 Sets

• NCERT Class 11 Maths Solution Ex – 1.2
• NCERT Class 11 Maths Solution Ex – 1.3
• NCERT Class 11 Maths Solution Ex – 1.4
• NCERT Class 11 Maths Solution Ex – 1.5
• NCERT Class 11 Maths Solution Ex – 1.6

1. Which of the following are sets? Justify your answer. 

(i) The collection of all months of a year beginning with the letter J.
Solution – The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identity a month that belongs to this collection. Hence, this collection is a set.

(ii) The collection of ten most talented writers of India.
Solution – The collection of ten most talented writer of India is not a well-defined collection because the criteria for determining a writer’s talent vary from person to person. Hence, this collection is not a set.

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

2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:

(i) 5 . . . A
Solution – 5 ∈ A

(ii) 8 . . . A
Solution – 8 ∉ A

(iii) 0 . . . A
Solution – 0 ∉ A

(iv) 4 . . .  A
Solution – 4 ∈ A

(v) 2 . . . A
Solution – 2 ∈ A

(vi) 10 . . .  A
Solution – 10 ∉ A

3. Write the following sets in roster form:

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

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

(i) (3, 6, 9, 12}
Solution – 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}
Solution – 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}
Solution – 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 …}
Solution – {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}
Solution – 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}.

5. List all the elements of the following sets:

(i) A = {x: x is an odd natural number}
Solution – 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}
Solution – 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}
Solution – 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”}
Solution – 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}
Solution – 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}.
Solution – 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}

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:

Solution – 

Go Back To Chapters