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

The NCERT solutions have been prepared by the subject experts at BYJU’S and are in accordance with the NCERT syllabus and guidelines. Exercise 1.2 of NCERT Solutions for Class 11 Maths Chapter 1- Sets is based on the following topics:

  1. The Empty Set: A set which does not contain any element is called the empty set or the null set or the void set
  2. Finite and Infinite Sets: A set which is empty or consists of a definite number of elements is called finite otherwise, the set is called infinite
  3. Equal Sets: Two sets A and B are said to be equal if they have exactly the same elements and we write A = B. Otherwise, the sets are said to be unequal and we write A ≠ B

The subject specialists stick to the syllabus while preparing the solutions. The problem-solving method provided in the examples is followed while preparing the NCERT Solutions for class 11 as well.

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

ncert solution class 11 chapter 1 sets ex 2 1
ncert solution class 11 chapter 1 sets ex 2 2
ncert solution class 11 chapter 1 sets ex 2 3
ncert solution class 11 chapter 1 sets ex 2 4

 

Class 11 Maths Chapter 1- Sets exercise 1.2 Solutioins

1. Which of the following are examples of the null set

(i) Set of odd natural numbers divisible by 2

(ii) Set of even prime numbers

(iii) {x: is a natural numbers, < 5 and > 7}

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

Solution:

(i) Set of odd natural numbers divisible by 2 is a null set as odd numbers are not divisible by 2.

(ii) Set of even prime numbers is not a null set as 2 is an even prime number.

(iii) {xx is a natural number, < 5 and > 7} is a null set as a number cannot be both less than 5 and greater than 7.

(iv) {yy is a point common to any two parallel lines} is a null set as the parallel lines do not intersect. Therefore, they have no common point.

2. Which of the following sets are finite or infinite

(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

Solution:

(i) The set of months of a year is a finite set as it contains 12 elements.

(ii) {1, 2, 3 …} is an infinite set because it has infinite number of natural numbers.

(iii) {1, 2, 3 …99, 100} is a finite set as the numbers from 1 to 100 are finite.

(iv) The set of positive integers greater than 100 is an infinite set as the positive integers which are greater than 100 are infinite.

(v) The set of prime numbers less than 99 is a finite set as the prime numbers which are less than 99 are finite.

3. State whether each of the following set is finite or infinite:

(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)

Solution:

(i) The set of lines which are parallel to the x-axis is an infinite set as the lines which are parallel to the x-axis are infinite.

(ii) The set of letters in the English alphabet is a finite set as it contains 26 elements.

(iii) The set of numbers which are multiple of 5 is an infinite set as the multiples of 5 are infinite.

(iv) The set of animals living on the earth is a finite set as the number of animals living on the earth is finite.

(v) The set of circles passing through the origin (0, 0) is an infinite set as infinite number of circles can pass through the origin.

4. In the following, state whether A = B or not:

(i) A = {abcd}; B = {dcba}

(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

(iii) A = {2, 4, 6, 8, 10}; B = {xis positive even integer and ≤ 10}

(iv) A = {xis a multiple of 10}; B = {10, 15, 20, 25, 30 …}

Solution:

(i) A = {abcd}; B = {dcba}

Order in which the elements of a set are listed is not significant.

Therefore, A = B.

(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

We know that 12 ∈ A but 12 ∉ B.

Therefore, A ≠ B

(iii) A = {2, 4, 6, 8, 10};

B = {xx is a positive even integer and x ≤ 10} = {2, 4, 6, 8, 10}

Therefore, A = B

(iv) A = {xx is a multiple of 10}

B = {10, 15, 20, 25, 30 …}

We know that 15 ∈ B but 15 ∉ A.

Therefore, A ≠ B

5. Are the following pair of sets equal? Give reasons.

(i) A = {2, 3}; B = {xis solution of x2 + 5+ 6 = 0}

(ii) A = {xis a letter in the word FOLLOW}; B = {yis a letter in the word WOLF}

Solution:

(i) A = {2, 3}; B = {xis solution of x2 + 5+ 6 = 0}

x2 + 5x + 6 = 0 can be written as

x(x + 3) + 2(x + 3) = 0

By further calculation

(x + 2) (x + 3) = 0

So we get

x = –2 or x = –3

Here

A = {2, 3}; B = {–2, –3}

Therefore, A ≠ B

(ii) A = {xis a letter in the word FOLLOW} = {F, O, L, W}

B = {yis a letter in the word WOLF} = {W, O, L, F}

Order in which the elements of a set which are listed is not significant.

Therefore, A = B.

6. From the sets given below, select equal sets:

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}

Solution:

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}

We know that

8 ∈ A, 8 ∉ B, 8 ∉ D, 8 ∉ E, 8 ∉ F, 8 ∉ G, 8 ∉ H

A ≠ B, A ≠ D, A ≠ E, A ≠ F, A ≠ G, A ≠ H

It can be written as

2 ∈ A, 2 ∉ C

Therefore, A ≠ C

3 ∈ B, 3 ∉ C, 3 ∉ E, 3 ∉ F, 3 ∉ G, 3 ∉ H

B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H

It can be written as

12 ∈ C, 12 ∉ D, 12 ∉ E, 12 ∉ F, 12 ∉ G, 12 ∉ H

Therefore, C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H

4 ∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H

Therefore, D ≠ E, D ≠ F, D ≠ G, D ≠ H

Here, E ≠ F, E ≠ G, E ≠ H

F ≠ G, F ≠ H, G ≠ H

Order in which the elements of a set are listed is not significant.

B = D and E = G

Therefore, among the given sets, B = D and E = G.


Access other exercise solutions of Class 11 Maths Chapter 1- Sets

Exercise 1.1 Solutions 6 Questions

Exercise 1.3 Solutions 9 Questions

Exercise 1.4 Solutions 12 Questions

Exercise 1.5 Solutions 7 Questions

Exercise 1.6 Solutions 8 Questions

Miscellaneous Exercise On Chapter 1 Solutions 16 Questions

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