**Question 1: Which of the following are sets? Justify our answer.**

**(i) The collection of all 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 batsmen 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 this Chapter.**

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

**Solution:**

(i)All months that begins with the letter J is a well-defined collection as one can easily identify whether a month begins with J or not.

Therefore, this collection is a set.

(ii)Ten most talented writers of India is not a well-defined collection as one writer’s talent cannotbe measured and it vary for person to person.

Therefore, this collection is not a set.

(iii)A team of eleven best cricket batsmen of the world is not a well-defined collection because one person can consider a batsman as best whereas other person may not consider it. There’s no measuring unit.

Therefore, this collection is not a set.

(iv)This collection is a well-defined collection as you can easily identify whether a boy belongs to your class or not.

Therefore, this collection is a set.

(v)The collection of all natural numbers less than 100 is a well-defined collection because it’s possible to decide whether a number is less than 100 or not.

Therefore, this collection is a set.

(vi)A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because one can definitely identify whether a book is written by Munshi Prem Chand or not.

Therefore, this collection is a set.

(vii)This collection is a well-defined collection because one can definitely identify which is an even integer and which is not.

Therefore, this collection is a set.

(viii)This collection is a well-defined collection because one can definitely identify whether a question belongs to this chapter or not.

Therefore, this collection is a set.

(ix)This collection of most dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal varies from person to person.

Therefore, this collection is not a set.

**Question 2: Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces:**

**(i) 5…A **

**(ii) 8…A **

**(iii) 0…A**

**(iv) 4…A **

**(v) 2…A **

**(vi) 10…A**

**Solution:**

(i)5 ∈ A

(ii)8 ∉ A

(iii)0 ∉ A

(iv)4 ∈ A

(v)2 ∈ A

(vi)10 ∉ A

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

**(i) A = {x: x is an integer and –3 < x < 7}.**

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

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

**(iv) D = {x: x 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.**

**Solution:**

(i)A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}

(ii)B = {1, 2, 3, 4, 5}

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

(iv)Prime factorization of 60 is60 = 22 × 31 × 51

D = {2, 3, 5}

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

(vi)F = {R, T, E, B}

**Question 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}**

**Solution:**

(i){3, 6, 9, 12}3 = 3*1, 6 = 3*2, 9 = 3*3, 12 = 3*4.

∴ Set builder form is

{x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}

(ii){2, 4, 8, 16, 32}We know that all the numbers can be written as following 2 = 21, 4 = 22, 8 = 23, 16 = 24, 32 = 25.

∴ Set builder form is

{x: x = 2n, n ∈ N and 1 ≤ n ≤ 5}

(iii){5, 25, 125, 625}We know that all the numbers can be written as following 5 = 51, 25 = 52, 125 = 53, and 625 = 54.

∴ Set builder form is

{x: x = 5n, n ∈ N and 1 ≤ n ≤ 4}

(iv){2, 4, 6 …}Given set is a set of all even natural numbers.

∴ Set builder form is

{x: x is an even natural number}

(v){1, 4, 9, 16, 25 … 100}We know that all the numbers can be written as following, 1 = 12, 4 = 22, 9 = 32 …100 = 102.

∴ Set builder form is

{x: x = n2, n ∈ N and 1 ≤ n ≤ 10}

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

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

**(ii) B = {x: x is an integer, -1/2 < x < 9/2}**

**(iii) C = {x: x is an integer, x ^{2 }≤ 4}**

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

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

**(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.**

**Solution:**

(i)A= {1, 3, 5, 7, 9 …}

(ii)B = {0,1,2,3,4}

(iii)We know that(–1)

^{2}= 1 ≤ 4(–2)

^{2}= 4 ≤ 4(–3)

^{2}= 9 > 40

^{2}= 0 ≤ 41

^{2}= 1 ≤ 42

^{2}= 4 ≤ 43

^{2}= 9 > 4∴ C = {–2, –1, 0, 1, 2}

(iv)D = {L, O, Y, A}

(v)E = {February, April, June, September, November}

(vi)F = {b, c, d, f, g, h, j}

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

(i) {1, 2, 3, 6} | (a) {x: x is a prime number and a divisor of 6} |

(ii) {2, 3} | (b) {x: x is an odd natural number less than 10} |

(iii) {M, A, T, H, E, I, C, S} | (c) {x: x is natural number and divisor of 6} |

(iv) {1, 3, 5, 7, 9} | (d) {x: x is a letter of the word MATHEMATICS} |

**Solution:**

(i)All the elements given in this set are natural numbers as well as the divisors of 6.

Therefore, (i) matches with (c).

(ii)We know that 2 and 3 are prime numbers. They are also the divisors of 6.

Therefore, (ii) matches with (a).

(iii)This set contains all the letters from the word MATHEMATICS.

Therefore, (iii) matches with (d).

(iv)This set contains odd natural numbers which are smaller than 10.

Therefore, (iv) matches with (b).