Sets

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, x² ≤ 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 x2 – 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.