# Sets - CBSE Class 11 Mathematics Solutions of Exercise 1.1 | Ncert Solutions of Class XI Maths 1.1

## Solutions of CBSE Class XI NCERT Mathematics

### Chapter 1, sets

#### CBSE Class 11 NCERT Mathematics Solutions of Exercise 1.1

(Cbse Class 11 Ncert Math Textbook Page 4)
(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.

Solution:
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because we can definitely identify a month that belongs to this collection. So, this collection is a set.
(ii) The collection of ten most talented writers of India is not a well-defined collection since the criteria for determining a writer’s talent could vary from person to person. So, 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 for determining a batsman’s talent will vary from person to person. Hence, this collection cannot be termed 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 each number that belongs to this collection is a definite number. 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. So, 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 and hence, this collection is a set.
(ix) The collection of most dangerous animals of the world is not a set. Because the criteria for determining the dangerousness of an animal can vary from person to person and the collection will also vary.

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

Solution: (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.

Solution:
(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.
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}
The elements of this set are 1, 2, 3, 4, and 5 only.
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}
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}

∴ 60 = 2 × 2 × 3 × 5
Hence, the elements of this set are 2, 3, and 5.
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. Hence, 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}

#### CBSE Class 11 Mathematics NCERT Solutions of Chapter 1, Sets Exercise 1.1

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}

Solution:
(i) {3, 6, 9, 12} = {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}
(ii) In the given set, 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25
∴ {2, 4, 8, 16, 32} = {x: x = 2n, n ∈ N and 1 ≤ n ≤ 5}
(iii) {5, 25, 125, 625}
It can be seen that 5 = 51 , 25 = 52 , 125 = 53 , and 625 = 54
Therefore, {5, 25, 125, 625} = {x: x = 5n, n ∈ N and 1 ≤ n ≤ 4}
(iv) {2, 4, 6 …} is a set of all even natural numbers.
∴ {2, 4, 6 …} = {x: x is an even natural number}
(v) {1, 4, 9 … 100}
In the given set of numbers, 1 = 12, 4 = 22, 9 = 32 …100 = 102.
∴ {1, 4, 9… 100} = {x: x = n2, n ∈ N and 1 ≤ n ≤ 10}

Question 5: List all the elements of the following sets:

Solution:
(i) A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}

(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}

Solution:
(i) – (c); Because all the elements of this set are natural numbers as well as the divisors of 6.
(ii) – (a); It can be seen that 2 and 3 are prime numbers and are also the divisors of 6.
(iii) – (d); Since all the elements of this set are letters of the word MATHEMATICS.

(iv) – (b); as all the elements of this set are odd natural numbers less than 10.