Class 11 - Chapter 1: Sets

NCERT Solution- Class 11 Mathematics Chapter 1 Sets

Exercise 1.1

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.

Solution:

The months of a year beginning with the letter J are January, June and July.

Therefore, the collection can be written as:

{January, June, July}

Since every element of the collection is clearly determined, the collection is well-defined.

Answer: It is a Set.

(ii) The collection of ten most talented writers of India.

Solution:

The term "most talented" is subjective and may vary from person to person. Different people may select different writers.

Hence the collection is not well-defined.

Answer: It is not a Set.

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

Solution:

The word "best" is subjective and different people may choose different players.

Therefore, the collection is not well-defined.

Answer: It is not a Set.

(iv) The collection of all boys in your class.

Solution:

The boys of a particular class can be identified exactly.

Hence the collection is well-defined.

Answer: It is a Set.

(v) The collection of all natural numbers less than 100.

Solution:

The collection can be written as:

{1, 2, 3, ..., 99}

Every element is clearly determined.

Answer: It is a Set.

(vi) A collection of novels written by the writer Munshi Prem Chand.

Solution:

The novels written by Munshi Prem Chand are fixed and identifiable.

Hence the collection is well-defined.

Answer: It is a Set.

(vii) The collection of all even integers.

Solution:

The collection can be represented as:

{..., -6, -4, -2, 0, 2, 4, 6, ...}

All elements satisfy the property of being even integers.

Answer: It is a Set.

(viii) The collection of questions in this chapter.

Solution:

The questions contained in a chapter are fixed and can be counted.

Hence the collection is well-defined.

Answer: It is a Set.

(ix) A collection of most dangerous animals of the world.

Solution:

The term "most dangerous" is subjective and may vary from person to person.

Hence the collection is not well-defined.

Answer: It is not a Set.

Question 2

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

Question 3

Write the following sets in roster form.

(i) A = {x : x is an integer and −3 ≤ x < 7}

Solution:

The integers satisfying −3 ≤ x < 7 are:

A = {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6}

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

Solution:

Natural numbers less than 6 are:

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:

The required two-digit numbers are:

17, 26, 35, 44, 53, 62, 71, 80

Therefore,

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

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

Solution:

Prime factorisation of 60:

60 = 2² × 3 × 5

Prime divisors of 60 are 2, 3 and 5.

Therefore,

D = {2, 3, 5}

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

Solution:

A set contains distinct elements only.

E = {T, R, I, G, O, N, M, E, Y}

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

Solution:

Repeated letters are written only once in a set.

F = {B, E, T, R}

Question 4

Write the following sets in set-builder form.

(i) {3, 6, 9, 12}

Solution:

{x : x = 3n, n ∈ ℕ and 1 ≤ n ≤ 4}

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

Solution:

{x : x = 2ⁿ, n ∈ ℕ and 1 ≤ n ≤ 5}

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

Solution:

{x : x = 5ⁿ, n ∈ ℕ and 1 ≤ n ≤ 4}

Final Answers

Question 1: Sets → (i), (iv), (v), (vi), (vii), (viii)

Question 1: Not Sets → (ii), (iii), (ix)

Question 2: 5 ∈ A, 8 ∉ A, 0 ∉ A, 4 ∈ A, 2 ∈ A, 10 ∉ A

Question 5

List all the elements of the following sets:

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

Solution:

Odd natural numbers are natural numbers which are not divisible by 2.

Therefore,

A = {1, 3, 5, 7, 9, 11, 13, ...}

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

Solution:

The integers lying between −1/2 and 9/2 are:

0, 1, 2, 3, 4

Therefore,

B = {0, 1, 2, 3, 4}

(iii) C = {x : x is an integer, x² ≤ 4}

Solution:

Given:

x² ≤ 4

Taking square roots,

−2 ≤ x ≤ 2

The integers satisfying the condition are:

−2, −1, 0, 1, 2

Therefore,

C = {−2, −1, 0, 1, 2}

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

Solution:

The letters in the word LOYAL are:

L, O, Y, A, L

Since repeated elements are written only once in a set,

D = {L, O, Y, A}

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

Solution:

Months not having 31 days are:

February, April, June, September and November.

Therefore,

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

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

Solution:

Letters before k are:

a, b, c, d, e, f, g, h, i, j

Among these, the consonants are:

b, c, d, f, g, h, j

Therefore,

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:

Matching Summary:

(i) → (c)

(ii) → (a)

(iii) → (d)

(iv) → (b)