Question

Write the following sets in the roaster from
(i) A = {x : x ∈ R, 2x + 11 = 15} (ii) B = {x | x^2 = x, x ∈ R}
(iii) C = {x | x is a positive factor of a prime number p}

Answer 1

i)  A= {2}

ii) B= {0,1}

iii) C= {1}

Answer 2

Answer:

We know that the factors of the prime numbers are 1 and the number itself.

The whole number of factors of the prime number is 2.

Step-by-step explanation:

(i) Given: A = {x∶ x ∈ R,2x + 11 = 15}

To find: Roster form of given set

2x + 11 = 15

⇒ 2x = 15 – 11

⇒ 2x = 4

⇒ x = 2

So, A = {2}

(ii) Given: B = {x | x^2  = x,x ∈ R}

To find: Roster form of given set

x^2  = x

⇒ x^2  – x = 0

⇒ x(x – 1) = 0

⇒ x = 0 or 1

So, B = {0,1}

(iii) Given: C = {x | x is a positive factor of the prime number p}

To find: Roster form of given set

Only possible positive factors of the prime number p are 1 and p itself.

Hence,

x = 0 or p

So, C = {0,p}

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