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**Exercise 1.1**

**1. Which of the following are sets? Justify your answer.**

**(i) The collection of all the months of a year beginning with the letter J.**

**(ii) The collection of ten most talented writers of India.**

**(iii) A team of eleven best-Cricket batmen of the world.**

**(iv) The collection of all boys in your class.**

**(v) The collection of all natural numbers less than 100.**

**(vi) A collection of novels written by the writer Munshi Prem Chand.**

**(vii) The collection of all even integers.**

**(viii) The collection of questions in the chapter.**

**(ix) A collection of most dangerous animals of the world.**

**Ans. (i) **The collection of all months of a year beginning with J is {January, June, July}, which is well defined and hence it forms a set.

**(ii) **The collection of most talented writers of India is not well defined because opinions about ‘most talented writers’ vary from person to person and hence it does not form a set.

**(iii) **A team of eleven best-cricket batmen of the world us not well defined because opinion about ‘best-cricket batsmen’ vary from person to person and hence it does not form a set.

**(iv) **The collection of all boys in your class is well defined and hence it forms a set.

**(v) **The collection of all natural numbers less than 100 is {1, 2, 3, ……., 99} which is well defined and hence it forms a set.

**(vi) **A collection of novels written by the writer Munshi Prem Chand is well defined and hence it forms a set.

**(vii) **The collection al all even integers is which is well defined and hence it forms a set.

**(viii) **The collection of questions in this chapter is well defined and hence it forms a set.

**(ix) **A collection of most dangerous animals of the world is not well defined because opinion about ‘most dangerous animals’ vary from person to person and hence it does not form a set.

**2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol **** or **** on the blank space:**

**(i) 5 _______ A **

**(ii) 8 _______ A **

**(iii) 0 _______ A**

**(iv) 4 _______ A **

**(v) 2 _______ A **

**(vi) 10 _______ A**

**Ans. **Given: A = {1, 2, 3, 4, 5, 6}

**(i) **5 is an element of set A

5 A

**(ii) **8 is not an element of set A

8 A

**(iii) **0 is not an element of set A

0 A

**(iv) **4 is an element of set A

4 A

**(v) **2 is an element of set A

2 A

**(vi) **10 is not an element of set A

10 A

**3. Write the following sets in roster form:**

**(i) A = {**** is an integer and ****}**

**(ii) B = {**** is a natural number less than 6}**

**(iii) C = {**** is a two-digit natural number such that the sum of its digits is 8}**

**(iv) D = {**** is a prime number which is divisor of 60}**

**(v) E = The set of all letters in the word TRIGONOMETRY**

**(vi) F = The set of all letters in the word BETTER**

**Ans. (i) **A = { is an integer and } A =

**(ii) **B = { is a natural number less than 6} B = {1, 2, 3, 4 5}

**(iii) **C = { is a two-digit natural number such that the sum of its digits is 8}

C = {17, 26, 35, 44, 53, 62, 71, 80}

**(iv) **D = { is a prime number which is divisor of 60}

D = {2, 3, 5}

**(v) **E = The set of all letters in the word TRIGONOMETRY

E = {T, R, I, G, O, N, O, M, E, T, R, Y}

**(vi) **F = The set of all letters in the word BETTER

F = {B, E, T, R}

**4. Write the following sets in the set-builder form:**

**(i) {3, 6, 9, 12} **

**(ii) {2, 4, 8, 16, 32} **

**(iii) {5, 25, 125, 625}**

**(iv) {2, 4, 6, ……} **

**(v) {1, 4, 9, ………, 100}**

**Ans. (i) **Let A = {3, 6, 9, 12}.

Here all objects of the set are natural numbers that are multiples of 3.

A =

**(ii) **Let B = {2, 4, 8, 16, 32}

Here all objects of the set are natural numbers that are power of 2.

B =

**(iii) **Let C = {5, 25, 125, 625}

Here all objects of the set are natural numbers that are power of 5.

C =

**(iv) **Let D = {2, 4, 6, ……}

Here all objects of the set are even natural numbers.

D =

**(v) **Let E = {1, 4, 9, ………, 100}

Here all objects of the set are perfect square.

D =

**5. List all the elements of the following sets:**

**(i) A = {**** is an odd natural number}**

**(ii) B = {**** is an integer, ****}**

**(iii) C = {**** is an integer, ****}**

**(iv) D = {**** is a letter in the word “LOYAL”}**

**(v) E = {**** is a month of a year not having 31 days}**

**(vi) F = {**** is a consonant in the English alphabet which precedes K}**

**Ans. (i) **A = { is an odd natural number}

A = {1, 3, 5, 7, ……..}

**(ii) **B = { is an integer, }

B = {0, 1, 2, 3, 4}

**(iii) **C = { is an integer, }

C =

**(iv) **D = { is a letter in the word “LOYAL”}

D = {L, O, Y, A}

**(v) **E = { is a month of a year not having 31 days}

E = {February, April, June, September, November}

**(vi) **F = { is a consonant in the English alphabet which precedes K}

F = {B, C, D, F, G, H, J}

**6. Match each of the set on the left in the roster form with the same set on the right described in the set-builder form:**

**(i) {1, 2, 3, 6} **

**(a) {**** is a prime number and a divisor of 6}**

**(ii) {2, 3} **

**(b) {**** is an odd natural number less than 10}**

**(iii) {M, A, T, H, E, I, C, S} **

**(c) {**** is a natural number and divisor of 6}**

**(iv) {!, 3, 5, 7, 9} **

**(d) {**** is a letter of word “MATHEMATICS”}**

**Ans. **The sets which are in set-builder form can be written as

**(a) **{ is a prime number and a divisor of 6} = {2, 3}

**(b) **{ is an odd natural number less than 10} = {1, 3, 5, 7, 9}

**(c) **{ is a natural number and divisor of 6} = {1, 2, 3, 6}

**(d) **{ is a letter of word “MATHEMATICS”} = {M, A, T, H, E, I, C, S}

Hence the correct matching is:

**(i)** (c)

**(ii)** (a)

**(iii)** (d)

**(iv)** (b)