NCERT Solutions for Exercise 1.2 Class 11 Maths Chapter 1 - Sets

# NCERT Solutions for Exercise 1.2 Class 11 Maths Chapter 1 - Sets

Edited By Vishal kumar | Updated on Oct 31, 2023 10:13 AM IST

## NCERT Solutions for Class 11 Maths Chapter 1: Sets Exercise 1.2- Download Free PDF

NCERT Solutions for Class 11 Maths Chapter 1: Sets Exercise 1.2- In the previous exercise, you have learned about the definition and representations of sets. In the NCERT solutions for Class 11 Maths chapter 1 exercise 1.2, you will learn about the different types of sets like empty sets, finite sets, infinite sets, equal sets, etc. The empty set is also called a null set or void sell. The definitions of the different types of sets are given before this exercise.

You must go through these definitions given in the NCERT textbook which will give you more clarity. You can solve exercise 1.2 Class 11 Maths problems which are quite basic based on the definitions only. You may find some difficulties while solving them. You can go through the exercise 1.2 class 11 maths solutions provided in this article. If you are looking for other classes as well, you can go to this NCERT Solutions link where you will get NCERT solutions from Class 6 to Class 12 for Science and Math.

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## NCERT Solutions for Class 11 Maths Chapter 1 – Sets Exercise 1.2

Access sets Class 11 Chapter 1 Exercise: 1.2

## Question:1(i) Which of the following are examples of the null set :

Set of odd natural numbers divisible by 2

No odd number is divisible by 2.

Hence, this is a null set.

Question:1(ii) Which of the following are examples of the null set :

Set of even prime numbers.

Even prime number = 2.

Hence, it is not a null set.

Question:1(iii) Which of the following are examples of the null set:

{ x : x is a natural numbers, $x< 5$ and $x> 7$ }

No number exists which is less than 5 and more than 7.

Hence, this is a null set.

Question:1(iv) Which of the following are examples of the null set :

{ y : y is a point common to any two parallel lines}

Parallel lines do not intersect so they do not have any common point.

Hence, it is a null set.

(i) The set of months of a year

(ii) {1, 2, 3, . . .}

(iii) {1, 2, 3, . . .99, 100}

(iv) ) The set of positive integers greater than 100.

(v) The set of prime numbers less than 99

(i) Number of months in a year are 12 and finite.

Hence,this set is finite.

(ii) {1,2,3,4.......} and so on ,this does not have any limit.

Hence, this is infinite set.

(iii) {1,2,3,4,5......100} has finite numbers.

Hence ,this is finite set.

(iv) Positive integers greater than 100 has no limit.

Hence,it is infinite set.

(v) Prime numbers less than 99 are finite ,known numbers.

Hence,it is finite set.

(i) The set of lines which are parallel to the x-axis

(ii) The set of letters in the English alphabet

(iii) The set of numbers which are multiple of 5

(iv) The set of animals living on the earth

(v) The set of circles passing through the origin (0,0)

(i) Lines parallel to the x-axis are infinite.

Hence, it is an infinite set.

(ii) Letters in English alphabets are 26 letters which are finite.

Hence, it is a finite set.

(iii) Numbers which are multiple of 5 has no limit, they are infinite.

Hence, it is an infinite set.

(iv) Animals living on earth are finite though the number is very high.

Hence, it is a finite set.

(v) There is an infinite number of circles which pass through the origin.

Hence, it is an infinite set.

Question:4(i) In the following, state whether A = B or not:

A = { a, b, c, d } B = { d, c, b, a }

Given
A = {a,b,c,d}

B = {d,c,b,a}
Comparing the elements of set A and set B, we conclude that all the elements of A and all the elements of B are equal.
Hence, A = B.

Question:4(ii) In the following, state whether A = B or not:

A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}

12 belongs A but 12 does not belong to B

12 $\in$ A but 12 $\notin$ B.

Hence, A $\neq$ B.

Question:4(iii) In the following, state whether A = B or not:

A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and $x \leq 10$}

Positive even integers less than or equal to 10 are : 2,4,6,8,10.

So, B = { 2,4,6,8,10 } which is equal to A = {2,4,6,8,10}

Hence, A = B.

Question:4(iv) In the following, state whether A = B or not:

A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }

Multiples of 10 are : 10,20,30,40,........ till infinite.

SO, A = {10,20,30,40,.........}

B = {10,15,20,25,30........}

Comparing elements of A and B,we conclude that elements of A and B are not equal.

Hence, A$\neq$ B.

Question:5(i) Are the following pair of sets equal ? Give reasons.

A = {2, 3}, B = {x : x is solution of $x^{2}$+ 5x + 6 = 0}

As given,

A = {2,3}

And,

$x^{2}+5x+6= 0$

$x\left ( x+3 \right ) + 2\left ( x+3 \right )= 0$

$( x+2 ) ( x+3)= 0$

x = -2 and -3

B = {-2,-3}

Comparing elements of A and B,we conclude elements of A and B are not equal.

Hence,A$\neq$B.

Question:5(ii) Are the following pair of sets equal ? Give reasons.

A = { x : x is a letter in the word FOLLOW}

B = { y : y is a letter in the word WOLF}

Letters of word FOLLOW are F,OL,W.

SO, A = {F,O,L,W}

Letters of word WOLF are W,O,L,F.

So, B = {W,O,L,F}

Comparing A and B ,we conclude that elements of A are equal to elements of B.

Hence, A=B.

A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2}

E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}

Compare the elements of A,B,C,D,E,F,G,H.

8 $\in$ A but $8\notin B,8\in C,8\notin D,8\notin E,8\notin F,8\notin G,8\notin H$

Now, 2$\in$ A but 2$\notin$C.

Hence, A$\neq$B,A$\neq$C,A$\neq$D,A$\neq$E,A$\neq$F,A$\neq$G,A$\neq$H.

3 $\in$ B,3$\in$D but 3$\notin$C,3$\notin$ E,3$\notin$F,3$\notin$G,3$\notin$H.

Hence,B$\neq$C,B$\neq$E,B$\neq$F,B$\neq$G,B$\neq$H.

Similarly, comparing other elements of all sets, we conclude that elements of B and elements of D are equal also elements of E and G are equal.

Hence, B=D and E = G.

## More About NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.2

Class 11th Maths Chapter 1 Exercise 1.2 consists of questions related to finding the different types of sets. There are six questions in this exercise based on the basic definitions of types of sets. There are some examples and definitions given before Class 11 Maths ch 1 ex 1.2 in the NCERT textbook. Solve these examples and exercise questions by yourself to get more clarity. These basic definitions will be useful in the upcoming exercises of this chapter.

Careers360 subject experts have crafted NCERT Solutions for Class 11 Maths Chapter 1, Exercise 1.2, aligned with the 2023-24 CBSE Syllabus. This exercise covers topics like the Empty Set, Finite and Infinite Sets, and Equal Sets, ensuring a methodical approach to problem-solving in line with the provided examples.

Also Read| Sets Class 11th Notes

## Benefits of NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.2

• Class 11 Maths Chapter 1 exercise 1.2 solutions are useful if you ever get doubts regarding the definition of different types of sets.
• NCERT syllabus Class 11th Maths chapter 1 exercise 1.2 are also useful in some other chapter like relations and functions, trigonometric functions, inverse trigonometric functions
• NCERT Solutions for Class 11 Maths chapter 1 exercise 1.2 can be used for reference.
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## Key Features of 11th Class Maths Exercise 1.2 Answers

1. Expert Preparation: The class 11 maths chapter 1 exercise 1.2 solutions are expertly crafted by subject specialists to provide accurate and reliable answers.

2. CBSE Syllabus Alignment: The class 11 ex 1.2 solutions are in strict accordance with the latest CBSE Syllabus for the academic year 2023-24.

3. Comprehensive Coverage: Class 11 maths ex 1.2 covers essential topics, including the Empty Set, Finite and Infinite Sets, and Equal Sets.

4. Problem-Solving Method: The ex 1.2 class 11 solutions follow a structured problem-solving method, consistent with the approach demonstrated in the examples for a thorough understanding.

## Subject Wise NCERT Exampler Solutions

Happy learning!!!

1. What is the definition of empty set ?

The set which doesn't contain any element is called an empty set.

2. Write an example of empty set ?

Set A = { x : 1<x<2 , x is a natural number  }

3. What is the definition of finite set ?

The set which contains the definitive number of elements is called a finite set.

4. Write an example of finite set ?

Set A = { 1,2,3,4,5,6,7,8} is an example of finite set.

5. What is the definition of infinite set ?

The set which contains the indefinite number of elements is called an infinite set.

6. Write an example of infinite set ?

Set A  = { n: n is natural number } is an example of infinite set.

7. What is the definition of equal set ?

Two sets A and B are said to be equal sets if every element of A is present in set B and every element of set B is present in set A.

8. Write an example of equal set ?

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

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

Set A and Set B are equal.

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