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 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.
(i), (iv), (v), (vi), (vii) and (viii) are sets.
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
(i) ∈ (ii) ∉ (iii) ∉ (iv) ∈ (v) ∈ (vi) ∉
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
(i) A = {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = {1, 2, 3, 4, 5}
(iii) C = {17, 26, 35, 44, 53, 62, 71, 80}
(iv) D = {2, 3, 5}
(v) E = {T, R, I, G, O, N, M, E, Y}
(vi) F = {B, E, T, R}
Write the following sets in 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}
(i) {x : x = 3n, n ∈ ℕ and 1 ≤ n ≤ 4}
(ii) {x : x = 2ⁿ, n ∈ ℕ and 1 ≤ n ≤ 5}
(iii) {x : x = 5ⁿ, n ∈ ℕ and 1 ≤ n ≤ 4}
(iv) {x : x is an even natural number}
(v) {x : x = n², n ∈ ℕ and 1 ≤ n ≤ 10}
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, x² ≤ 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 precedes k}
(i) A = {1, 3, 5, …}
(ii) B = {0, 1, 2, 3, 4}
(iii) 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}
Match each of the set on the left in roster form with the same set on the right described in set-builder form:
(i) {1, 2, 3, 6}
(ii) {2, 3, 5, 7, 11}
(iii) {M, A, T, H, E, I, C, S}
(iv) {1, 3, 5, 7}
(i) ↔ (c) (ii) ↔ (a) (iii) ↔ (d) (iv) ↔ (b)