**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}