**NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1**

**Ex 1.1 Class 11 Maths 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 world.

**Solution.
(i)** The collection of all months of a year beginning with J is
{January, June, July}, which is well-defined and hence it is a set.

**(ii)**The collection of most talented writers of India is not well-defined because opinions about ‘most talented writers’ may vary from person to person and hence it is not a set.

**(iii)**A team of eleven best-cricket batsmen of the world is not well-defined because opinions about ‘best-cricket batsmen’ may vary from person to person and hence it is not a set.

**(iv)**The collection of all boys in your class is well-defined and hence it is a set.

**(v)**The collection of all natural numbers less than 100 is {1, 2, 3, 4, …………, 99}, which is well-defined and hence it is a set.

**(vi)**A collection of novels written by the writer Munshi Prem Chand is well-defined and hence it is a set.

**(vii)**The collection of all even integers is {…………..,-4, -2, 0, 2, 4,……….. } which is well-defined and hence it is a set.

**(viii)**The collection of questions in this chapter is well-defined and hence it is a set.

**(ix)**A collection of most dangerous animals of the world is not well-defined because opinions about ‘most dangerous animals’ may vary from person to person and hence it is not a set.

**Ex 1.1 Class
11 Maths Question 2.**

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

**(i)****(ii)**8…A

**(iii)**0…A

**(iv)**4…A

**(v)**2…A

**(vi)**10…A

**Solution.****
(i) **Since 5 is the element
of set A. ∴ 5

**∈**A.

**(ii)**Since 8 is not the element of set A. ∴ 8 ∉ A

**(iii)**Since 0 is not the element of set A ∴ 0 ∉ A.

**(iv)**Since 4 is the element of set A. ∴ 4 ∈ A.

**(v)**Since 2 is the element of set A. ∴ 2 ∈ A.

**(vi)**Since 10 is not the element of set A. ∴ 10 ∉ A.

**Ex 1.1 Class 11
Maths Question 3.**

Write
the following sets in roster form:**A = {x: x is an integer and -3 < x < 7}**

**(i)****(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}

Since integers lying between -3 and 7 are
-2, -1, 0, 1, 2, 3, 4, 5, 6.

∴ A = {-2, -1, 0, 1, 2, 3, 4, 5, 6}.

**(ii)** B = {x: x is a natural number less
than 6}

Since natural numbers less than 6 are 1, 2, 3, 4, 5.

∴ 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}

Since two-digit natural numbers such that the sum of its digits is 8 are 17,
26, 35, 44, 53, 62, 71, 80.

∴ C = {17, 26, 35, 44, 53, 62, 71, 80}

**(iv)** D = {x: x is a prime number which is divisor of 60}

Since prime numbers which are divisors of 60 are 2, 3, 5.

∴ D = {2, 3, 5}

**(v)** F = The set of all letters in the
word TRIGONOMETRY

Since the letters in the word
TRIGONOMETRY are T, R, I, G, O, N, M, E, Y.

∴ E = (T, R, I, G, O, N, M, E, Y}

**(vi)** F = The set of all letters in the
word BETTER

The word BETTER is formed by
using the letters B, E, T, R.

∴ F = (B, E, T, R}

**Ex 1.1 Class 11
Maths Question 4.**

Write
the following sets in the set-builder form:**{3, 6, 9, 12}**

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

**(iii)**{5, 25, 125, 625}

**(iv)**{2, 4, 6, …}

**(v)**{1, 4, 9, …….., 100}

**Solution.**

**(i)** Let
A = (3, 6, 9, 12}

All elements of the set are natural numbers that are multiples of 3.

∴ A = (x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}

**(ii)** Let B = (2, 4, 8, 16, 32} = (2^{1},
2^{2}, 2^{3}, 2^{4}, 2^{5}}

∴ B = {x: x = 2^{n}, n ∈ N and 1 ≤ n ≤ 5}

**(iii)** Let C = (5, 25, 125, 625} = (5^{1},
5^{2}, 5^{3}, 5^{4}}

∴ C = {x: x = 5^{n}, n ∈ N and 1 ≤ n ≤ 4}

**(iv)** Let D = (2, 4, 6, …}

All elements of the set are even natural numbers.

∴ D = (x: x is an even natural number}

**(v)** Let E = {1, 4, 9, ………., 100}

All elements of the set are perfect squares.

∴ E = {x: x = n^{2}, n ∈ N and 1 ≤ n ≤ 10}

**Ex 1.1 Class 11 Maths Question 5.**

List
all the elements of the following sets:**A = {x: x is an odd natural number}**

**(i)****(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}

**Solution.**

**(i)** A
= {x: x is an odd natural number}

∴ A = {1, 3, 5, 7, ………}

**(ii)** B = {x: x is an integer, −1/2 < x
< 9/2}

∴ B = {0, 1, 2, 3, 4}

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

x^{2} ≤ 4 ⇒ -2 ≤ x ≤ 2

∴ C = {-2, -1, 0, 1, 2}

**(iv)** D = {x: x is a letter in the word
“LOYAL”}

∴ D = {L, O, Y, A}

**(v)** E = {x: x is a month of a year not
having 31 days}

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

**(vi)** F = {x: x is a consonant in the
English alphabet which precedes k}

∴ F = {b, c, d, f, g, h, j}

**Ex 1.1 Class 11
Maths 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:**{1, 2, 3, 6}**

**i.****(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),

**(ii)** →
(a),

**(iii)** →
(d),

**(iv)** →
(b).

**Related Links:**

**NCERT Solutions for Maths Class 9**