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

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

Set of odd natural numbers divisible by 2

Answer:

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.

Answer:

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 }

Answer:

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}

Answer:

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

Hence, it is a null set.

Question: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

Answer:

(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.

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

(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)

Answer:

(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 }

Answer:

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}

Answer:

12 belongs A but 12 does not belong to B

12 ∈ A but 12 ∉ B.

Hence, A ≠ 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≤10}

Answer:

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, . . . }

Answer:

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≠ B.

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

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

Answer:

As given,

A = {2,3}

And,

x2+5x+6=0

x(x+3)+2(x+3)=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≠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}

Answer:

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.

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:

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

8 ∈ A but 8∉B,8∈C,8∉D,8∉E,8∉F,8∉G,8∉H

Now, 2∈ A but 2∉C.

Hence, A≠B,A≠C,A≠D,A≠E,A≠F,A≠G,A≠H.

3 ∈ B,3∈D but 3∉C,3∉ E,3∉F,3∉G,3∉H.

Hence,B≠C,B≠E,B≠F,B≠G,B≠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.