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}

2	60
2	30
3	15
	5

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}