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**Exercise 1.2**

**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) {**** is a natural number, **** and ****}**

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

**Ans. (i) **Set of odd natural numbers divisible by 2 is an empty set because odd natural numbers are not divisible by 2.

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

**(iii) **{ is a natural number, and } is an empty set because there is no natural number which satisfies simultaneously and .

**(iv) **{ is a point common to any two parallel lines} is an empty set because two parallel lines do not have a 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.**

**Ans. (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.

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

**(i) The set of lines which are parallel to the ****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).**

**Ans. (i) **The set of lines which are parallel to the axis is an infinite set because we can draw infinite number of lines parallel to 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 every 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 through origin in different radii.

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

**(i) A = **** B = **

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

**(iii) A = {2, 4, 6, 8, 10} B = {**** is a positive even integer and ****}**

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

**Ans. (i) **A = and B = are equal sets because order of elements does not change a set. Therefore, A = B =

**(ii) **A = {4, 8, 12, 16} and B = {8, 4, 16, 18} are not equal sets because 12 A, 12 B and 18 B, 19 A

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

**(iv) **A = { 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, 15 A.

**5. Are the following pairs of sets equal? Give reason.**

**(i) A = {2, 3} and B = {**** is a solution of ****}**

**(ii) A = :**** is a letter in the word FOLLOW}**

**B = { is a letter in the word WOLF}**

**Ans. (i) **A = {2, 3} and B

= { is a solution of }

Here

B =

Therefore, A and B are not equal sets.

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

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

Therefore, A = B = {F, O, L, W}

**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 = **

**F = **

**G = **

**H = {0, 1}**

**Ans. **From the given sets, Set B and D have same elements and also sets E and G have same element.

Mast