Write each of the following sets in Roster form :
(i) A = set of all prime numbers between 70 and 100.
(ii) B = set of all whole numbers less than 8.
(iii) C = set of all integers lying between -7 and 2.
(iv) D = set of all composite numbers between 23 and 33.
(v) E = set of letters in the word, 'MATHEMATICS'.
(vi) F = set of consonants in the word, 'SECONDARY'.
(vii) G = set of vowels in the word, 'INTERMEDIATE'.
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Question

Write each of the following sets in Roster form :
(i) A = set of all prime numbers between 70 and 100.
(ii) B = set of all whole numbers less than 8.
(iii) C = set of all integers lying between -7 and 2.
(iv) D = set of all composite numbers between 23 and 33.
(v) E = set of letters in the word, 'MATHEMATICS'.
(vi) F = set of consonants in the word, 'SECONDARY'.
(vii) G = set of vowels in the word, 'INTERMEDIATE'.

KnowledgeBoat · Accepted Answer

(i) A = {x : x is an integer, -3 x 4}. Integers greater than -3 and less than or equal to 4 are -2, -1, 0, 1, 2, 3, 4. A = {-2, -1, 0, 1, 2, 3, 4}, n(A) = 7 (ii) B = {x : x ∈ N, 3x - 6 9}. 3x - 6 9 ⇒ 3x 9 + 6 ⇒ 3x 15 ⇒ x ⇒ x 5. Since x is a natural number (N), x can be 1, 2, 3, 4. B = {1, 2, 3, 4}, n(B) = 4 (iii) C = {x : x = n2, n ∈ N, 10 n 16}. n can be 11, 12, 13, 14, 15. Calculating x(n2) = (11)2, (12)2, (13)2, (14)2, (15)2 = (11 x 11), (12 x 12), (13 x 13), (14 x 14), (15 x 15) = 121, 144, 169, 196, 225. C = {121, 144, 169, 196, 225}, n(C) = 5 (iv) D = {x : x ∈ W, x - 3 2}. x - 3 2 ⇒ x D = {0, 1, 2, 3, 4}, n(D) = 5 (v) E = {x : x = 2n - 1, n ∈ N and n 6}. n 6, so n = 1, 2, 3, 4, 5. Calculating x = (2n - 1): For n = 1, x = 2(1) - 1 = 1 For n = 2, x = 2(2) - 1 = 3 For n = 3, x = 2(3) - 1 = 5 For n = 4, x = 2(4) - 1 = 7 For n = 5, x = 2(5) - 1 = 9 E = {1, 3, 5, 7, 9}, n(E) = 5 (vi) F = {x : x is a letter in the word 'COMMON'}. The letters in 'COMMON' are C, O, M, M, O, N. Removing repeated letters, we get C, O, M, N. F = {C, O, M, N}, n(F) = 4 (vii) G = {x : x is a primary colour}. The primary colours are Red, Blue, and Yellow. G = {Red, Blue, Yellow}, n(G) = 3 (viii) H = {x : x is a digit in the numeral 2362}. The digits in 2362 are 2, 3, 6, 2. Removing the repeated digit '2', we get 2, 3, 6. H = {2, 3, 6}, n(H) = 3 (ix) J = . n can be 5, 6, 7, 8, 9. Calculating x = : For n = 5, For n = 6, For n = 7, For n = 8, For n = 9, , n(J) = 5

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