**Question 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: x is a natural number, x ≤ 5 and x > 7}**(iv)**{y: y is a point common to any two parallel lines}

**Solution.**

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

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

**(iii)** {x: x is a natural number, x < 5 and x >7} is a null set because there is no natural number which satisfies x < 5 and x > 7 simultaneously,

**(iv)** [y: y is a point common to any two parallel lines) is a null set because two parallel lines do not have any common point.

**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

**Solution.**

**(i)** The set of months of a year is finite set because there are 12 months in a year.

**(ii)** {1, 2, 3, …} is an infinite set because there are infinite elements in the set.

**(iii)** {1, 2, 3, …, 99, 100) is a finite set because the set contains finite number of elements.

**(iv)** The set of positive integers greater than 100 is an infinite set because there are infinite

number of positive integers greater than 100.

**(v)** The set of prime numbers less than 99 is a finite set because the set contains finite number of elements.

**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)

**Solution.**

**(i)** The set of lines which are parallel to the x-axis is an infinite set because we can draw infinite number of lines parallel to x-axis.

**(ii)** The set of letters in the English alphabet is a finite set because there are 26 letters in the English alphabet.

**(iii)** The set of numbers which are multiple of 5 is an infinite set because there are infinite multiples of 5.

**(iv)** The set of animals living on the earth is a finite set because the number of animals living on the earth is very large but finite.

**(v)** The set of circles passing through the origin (0, 0) is an infinite set because we can draw infinite number of circles passing through origin of different radii.

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

**(i)**A = {a, b, c, d};B = {d, c, b, a}**(ii)**A = {4, 8, 12, 16};B = {8, 4, 16, 18}**(iii)**A = {2, 4, 6, 8, 10} ;B = {x : x is positive even integer and x≤ 10}**(iv)**A = {x: x isa multiple of 10} ;B = {10, 15, 20, 25, 30,…}

**Solution.**

**(i)** A = {a, b, c, d} and B = {d, c, b, a} are equal sets because order of elements does not changes a set.

∴ A = B = [a, b, c, d}.

**(ii)** A = {4, 8, 12, 16} and B = {8, 4, 16, 18} are not equal sets because 12 ∈ A but 12 ∉ B and 18 ∉ B but 18 ∉ A.

**(iii)** A = {2, 4, 6, 8,10} and B = {x: x is a positive even integer and x ≤ 10) which can be written in roster form as B = (2, 4, 6, 8, 10) are equal sets.

∴ A = B = {2, 4, 6, 8,10).

**(iv)** A = {x: x is a multiple of 10) can be written in roster form as A = {10, 20, 30, 40,…….. } and

B – {10, 15, 20, 25, 30, ………..} are not equal sets because 15 ∈ B but 15 ∉ A.

**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}

- B={x: x is solution of x
**(ii)**A = {x: x is a letter in the word FOLLOW}- B = {y: y is a letter in the word WOLF}

**Solution.**

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

Now, x^{2} + 5x + 6 = 0 ⇒ x^{2} + 3x + 2x + 6 = 0 ⇒ (x + 3)(x + 2) = 0 ⇒ x = -3, -2

∴ B = {-2, -3}

Hence, A and B are not equal sets.

**(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}

Hence, A = B = {F, O, L, W}.

**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}

**Solution.**

From the given sets, we see that sets B and D have same elements and also sets E and G have same elements.

∴ B = D = {1 ,2, 3, 4} and E = G = {-1, 1}.