Question

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. 

Answer 1

(i) A = {x: x is an integer and –3 < x < 7} The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only. Therefore, the given set can be written in roster form as A = {–2, –1, 0, 1, 2, 3, 4, 5, 6} 

(ii) B = {x: x is a natural number less than 6} The elements of this set are 1, 2, 3, 4, and 5 only. Therefore, the given set can be written in roster form as B = {1, 2, 3, 4, 5} 

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8} The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only. Therefore, this set can be written in roster form as C = {17, 26, 35, 44, 53, 62, 71, 80} 

(iv) D = {x: x is a prime number which is a divisor of 60} 60 = 2 × 2 × 3 × 5 The elements of this set are 2, 3, and 5 only. Therefore, this set can be written in roster form as D = {2, 3, 5}. 

(v) E = The set of all letters in the word TRIGONOMETRY There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated. Therefore, this set can be written in roster form as E = {T, R, I, G, O, N, M, E, Y} 

(vi) F = The set of all letters in the word BETTER There are 6 letters in the word BETTER, out of which letters E and T are repeated. Therefore, this set can be written in roster form as F = {B, E, T, R}