Question:
Write the following sets in the roaster form:
(i) A = {x : x ∈ R, 2x + 11 = 15}
(ii) B = {x | x2 = x, x ∈ R}
(iii) C = {x | x is a positive factor of a prime number p}
Solution:
(i) According to the question,
A = {x : x ∈ R, 2x + 11 = 15}
Roster form,
2x + 11 = 15
⇒ 2x = 15 – 11
⇒ 2x = 4
⇒ x = 2
Hence, A = {2}
(ii) According to the question,
B = {x | x2 = x, x ∈ R}
Roster form,
x2 = x
⇒ x2 – x = 0
⇒ x(x – 1) = 0
⇒ x = 0 or 1
Hence, B = {0, 1}
(iii) According to the question,
C = {x | x is a positive factor of a prime number p}
Roster form,
Only possible positive factors of a prime number p = 1 and p itself.
Therefore,
x = 1 or p
Hence, C = {1, p}