Write the following sets in the roster form.
(a) A = {x : x ∈ W, x ≤ 5}
(b) B = {x : x ∈ I, -3 < x < 3)
(c) C = {x : x is divisible by 12}
(d) D = {x : x = 3p, p ∈ W, p ≤ 3}
(e) E = {x : x = a2, a ∈ N, 3 < a < 7}
(f) F = {x : x = n/(n + 1), n ∈ N and n ≤ 4}
(g) G = {x : x ∈ N, 3x - 2 < 5}
(h) J = {x : x ∈ N, x2 < 16}
(i) K = {x : x is a prime number which is a divisor of 42}
(j) H = {x : x is a 2-digit natural number such that the sum of its digits is 5}
Answers
Step-by-step explanation:
(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 natural numbers less than 6 are So, the elements of this set are 1, 2, 3, 4, and
1,2,3,4,5
5 only.
Therefore, the given set can be written in roster from as
B = {1, 2, 3, 4, 5}
(iii) C ={x: x is a two-digit natural number such tha
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 c
2 | 60
2130
315
515
| 1
..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 the letters, T, R, and O are repeated. And we write the repeated letters once only.
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}