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

- (i) The collection of all boys in your class.
- (ii) The collection of all even integers.
- (iii) The collection of nine most talented writers of India.
- (iv) A team of eleven best-cricket batsmen of the world.
- (v) A collection of novels written by the writer Rabindranath Tagore.
- (vi) The collection of all natural numbers less than 100.
- (vii) The collection of questions in this Chapter.
- (viii) The collection of all the months of a year beginning with the letter F.
- (ix) A collection of most dangerous animals of the world.

**Exercise 2**. Write the following sets in roster form:

- (i) F = The set of all letters in the word BETTER
- (ii) E = The set of all letters in the word TRIGONOMETRY
- (iii) B = {
*x*:*x*is a natural number less than 6} - (iv) D = {
*x*:*x*is a prime number which is divisor of 60} - (v) A = {
*x*:*x*is an integer and –3 ≤*x*< 7} - (vi) C = {
*x*:*x*is a two-digit natural number such that the sum of its digits is 8}

**Exercise 3**. Write the following sets in the set-builder form:

- (i) {2, 4, 6, . . .}
- (ii) {3, 6, 9, 12}
- (iii) {1, 4, 9, . . ., 100}
- (iv) {2, 4, 8,16, 32}
- (v) {5, 25, 125, 625}

**Exercise 4**. List all the elements of the following sets:

- (i) A = {
*x*:*x*is an odd natural number} - (ii) A = {
*x*:*x*is an even natural number} - (iii) B = {
*x*:*x*is an integer,*–*1/2 <*x*< 11/2} - (iv) C = {
*x*:*x*is an integer,*x*^{2}≤ 9} - (v) D = {
*x*:*x*is a letter in the word LOYAL} - (vi) E = {
*x*:*x*is a month of a year not having 31 days} - (vii) F = {
*x*:*x*is a consonant in the English alphabet which precedes*k*}

**Exercise 5**. 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) {M, A, T, H, E, I, C, S} | (b) {x : x is natural number and divisor of 6} |

(iii) {1, 3, 5, 7, 9} | (c) {x : x is an odd natural number less than 10} |

(iv) {2, 3} | (d) {x : x is a letter of the word MATHEMATICS} |

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

(i) {P, R, I, N, C, A, L} | (a) { x : x is a positive integer and is a divisor of 18} |

(ii) {M, A, T, H, E, I, C, S} | (b) { x : x is an integer and x^{2} – 9 = 0} |

(iii) { 0 } | (d) {x : x is a letter of the word PRINCIPAL} |

(iv) {1, 2, 3, 6, 9, 18} | (c) {x : x is an integer and x + 1 = 1} |

**Exercise 7**. State True or False for the following statements.

- (a) If
*A*is any set, then*A*⊂*A*. - (b) Given that
*M*= {1, 2, 3, 4, 5, 6, 7, 8, 9} and if*B*= {1, 2, 3, 4, 5, 6, 7, 8, 9}, then*B*⊄*M*. - (c) The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.
- (d)
**Q**È**Z**=**Q**, where**Q**is the set of rational numbers and**Z**is the set of integers. - (e) Let sets
*R*and*T*be defined as*R*= {*x*Î**Z**|*x*is divisible by 2} and*T*= {*x*Î**Z**|*x*is divisible by 6}. Then*T*⊂*R*. - (f) Given
*A*= {0, 1, 2},*B*= {*x*Î**R**| 0 ≤*x*≤ 2}. Then*A*=*B*.

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