Write the following sets in the roaster form:(i) A = {x : x ∈ R, 2

1.	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}
Answer» (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}

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}

Answer»

(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}