NCERT Solution and Introduction of Class 11 Maths Chapter 1 (Sets) Exercise 1.1

In this post, I will teach you Class 11 Maths Chapter 1 (Sets) Exercise 1.1. If you learn all the introduction parts of Chapter 1 (Sets) you will easily solve all the exercises in Chapter 1. The solutions given in this post are easy and simple and I also provide you with an explanation of every question in exercise 1.1.

Introduction of Chapter 1 (Sets)

What do mean by Sets?

A set is a well-defined Collection of objects. A Set is represented in the form {} Curly Brackets.

Example of Sets

A set of natural odd numbers between 1 to 10. {1, 3, 5, 7, 9}
A set of all-boys in your class.
A set of all the vowels in the English alphabet. {a, e, i, o, u}

Examples of not Possible sets

A set of smart boys in your school.
A set of beautiful rivers in India.

(Belongs to and Not Belongs to) symbol in Set

Let’s take some examples to understand the belongs to and not belongs to symbol in sets.

A set of natural odd numbers between 1 to 10. {1, 3, 5, 7, 9} and 1 ∈ to the set and 2 doesn’t ∉ the set.
w ∈ {w, i, n, n, e, r} but a ∉ {w, i, n, n, e, r}.

Representation of Sets

Sets in represented in two types-

Set Builder form
Roaster(Tabular from)

Example of Set Builder form

{x: x is less than 6 and x ∈ N} (N is Natural Number)
{x: x is an even number less than 10 and x ∈ N}

An example of a Roaster from

A = {1, 2, 3, 4, 5}
B= {2, 3, 6, 8}

Cardinality of Set

The meaning of Cardinality is the number of elements present in a particular set. For example, A = {1, 2, 3, 4, 5} A has 5 elements so the cardinality in set A is 5.

Notation– n(A) means the number of elements in set A.

Class 11 Maths 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.

Yes, it is a set. {January, June, July}

(II) The collection of the ten most talented writers of India.

No, it is not a set because the answer to the question may change from person to person.

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

No, it is not a set because the answer to the question may change from person to person.

(IV) The collection of all boys in your class

Yes, it is a set because your class has a fixed amount of number of boys.

(V) The collection of an all-natural number less than 100

Yes, it is a set. {1, 2, 3, 4,……..99}

(VI) A Collection of novels written by the writer Munshi Prem Chand.

Yes, it is a set because the collection of novels of Munshi Prem Chand is well-defined.

(VII) The collection of all even integers.

Yes, it is a set because the collection of integers is well-defined.

(VIII) The collection of questions in this chapter.

Yes, it is a set because the collection of questions in this chapter is fixed.

(IX) A Collection of the most dangerous animals in the world.

No, it is not a set because the answer to the question may change from person to person.

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

(I) 5………A (∈)

(II) 8……..A (∉)

(III) 0……A (∉)

(IV) 4……A (∈)

(V) 2……A (∈)

(VI) 10….A (∉)

Question 3 Write the following in roster form:

(I) A = {x : x is an integer and -3 ≤ x ≥ 7}

A = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}

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

B= {1, 2, 3, 4, 5}

(III) C = {x : x is a two-digit natural such that the sum of its digit is 8}

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

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

D = {2, 3, 5}

(V) E= the set of all letters in the word TRIGONOMETRY.

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

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

F= {B, E, T, R}

Question 4 Write the following sets in set builder form

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

{ x : x = 3n, n∈N and 1 ≤ n ≤ 4}

(II) {2, 4, 6, 8, 16, 32}

{x : x = 2ⁿ n∈N 1 ≤ n ≤ 5}

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

{x : x = 5ⁿ n∈N and 1 ≤ n ≤ 4}

(IV) {2, 4, 6…..}

{x : x is an even natural number}

(V) {1, 4, 9,…100}

{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}

A = {1, 3, 5,……}

(ii) B = {x: x is an integer, -1/2 < x < 9/2}
-1/2 is -0.5 and 9/2 is 4.5
B = {0, 1, 2, 3, 4}

(iii) C = {x: x is an integer, x² ≤ 4}
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 proceeds k}
F = {b, c, d, f, g, h, j}

Match each of the sets on the left in the roster form with the same set on the right described in the 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 a natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x: x is a letter of the word MATHEMATICS}

Answers
(i) Matches c
(ii) Mathes a
(iii) Mathes d
(iv) matches b