# 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 Set**s

- 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 = 2^{n} n**∈**N 1 ≤ n ≤ 5}

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

{x : x = 5^{n} 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