1. Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2
This is a null set because no odd number is divisible by 2.

(ii) Set of even prime numbers
Set of even prime numbers={2}
This is not a null set.

(iii) { x : x is a natural numbers, x < 5 and x > 7 }
This is a null set because a number cannot be less than 5 and also greater than 7.

(iv) { y : y is a point common to any two parallel lines}
This is a null set because two parallel lines do not intersect.

2. Which of the following sets are finite or infinite
(i) The set of months of a year
The set of months of a year has 12 elements. So this is a finite set.

(ii) {1, 2, 3, . . .}
The set has infinite natural numbers. So this is an infinite set.

(iii) {1, 2, 3, . . .99, 100}
The set has elements from 1 to 100. So this set is a finite set.

(iv) The set of positive integers greater than 100
There are infinite positive numbers greater than 100. So this is an infinite set

(v) The set of prime numbers less than 99
Prime numbers less than 99 is a finite number. So this is a finite set.

3. State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
Lines parallel to x-axis are infinite in number. So this is an infinite set.

(ii) The set of letters in the English alphabet
The set of letters in English alphabet has 26 elements. So this is a finite set.

(iii) The set of numbers which are multiple of 5
Multiple of 5 are infinite in number. So this is an infinite set.

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

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

4. In the following, state whether A = B or not:
(i) A = { a, b, c, d } B = { d, c, b, a }
Both sets have same elements. ∴ A=B

(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}
12∈ A and 12∉B. ∴ A≠B

(iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10}
A={2,4,6,8,10}, B={2,4,6,8,10}. ∴ A=B

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

5. Are the following pair of sets equal ? Give reasons.
(i) A = {2, 3}, B = {x : x is solution of $\displaystyle \small x^{2}$ + 5x + 6 = 0}
$\displaystyle \small x^{2}$ + 5x + 6 = 0
$\displaystyle \small x^{2}$ + 3x+2x + 6 = 0
x(x+3)+2(x+3)=0
(x+3)(x+2)=0
x=-3 or x=-2
A={2,3}, B={-2,-3}. ∴ A≠B

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

2∈ A, 2∉C
∴ A≠C

2∈B, 2∉C, 2∉E, 2∉F, 2∉G, 2∉H
∴ B≠C, B≠E, B≠F, B≠G, B≠H

14∈ C, 14∉D, 14∉E, 14∉F, 14∉G, 14∉H
∴ C≠D, C≠E, C≠F, C≠G, C≠H

3∈D, 3∉E, 3∉F, 3∉G, 3∉H
∴ D≠E, D≠F, D≠G, D≠H

-1∈ E, -1∉F, -1∉H
∴E≠F, E≠H

a∈F, a∉ G, a∉H
∴F≠G, F≠H

-1∈G, -1∉H
∴G≠H

Among the given sets, B=D and E=G