NCERT Solutions for Exercise 1.2, Class 11, Maths

Exercise 1.2 Sets
Question and Answers
Class 11 – Maths

Class	Class 11
Subject	Mathematics
Chapter Name	Sets
Chapter No.	Chapter 1
Exercise	Exercise 1.2
Category	Class 11 Maths NCERT Solutions

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

(i) Set of odd natural numbers divisible by 2

(i) There is no odd number that will be divisible by 2 and so this set is a null set.

(ii) Set of even prime numbers

(ii) There was an even number 2, which will be the one and only even prime number. So the set contains an element. So it is not a null set.

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

(iii) There was no number that will be less than 5 and greater than 7 simultaneously. So it is a null set.

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

(iv) The parallel lines do not intersect each other. So it does not have a common point of intersection. So it is a null set.

Question 2 Which of the following sets are finite or infinite

(i) The set of months of a year

(i) A year has twelve months which has defined number of elements. Therefore, the set of months of a year is finite.

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

(ii) The set consists of an infinite number of natural numbers. Therefore, the set  {1, 2, 3 …..} is infinite since it contains an infinite number of elements.

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

(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

(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

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

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

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

(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

(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

(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

(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)

(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.

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

(i) A = { a, b, c, d } B = { d, c, b, a }

(i) A = {a, b, c, d}; B = {d, c, b, a}

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}

(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 = { x : x is positive even integer and x ≤ 10}

(iii) A = {2, 4, 6, 8, 10};

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

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

(iv) A = {x: x is a multiple of 10}

B = {10, 15, 20, 25, 30 …}

We know that 15 ∈ B but 15 ∉ A. Therefore, A ≠ B

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

(i) A = {2, 3}, B = {x : x is solution of x 2 + 5x + 6 = 0}

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

x² + 5x + 6 = 0 can be written as  x(x + 3) + 2(x + 3) = 0

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

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

B = {y: y is 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.

Question 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}

Answer 

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.