If x ∈ N and 10 < x < 20, and x is a prime number, then which of the following represents the list form of the set of such numbers?

Question: If x ∈ N and 10 < x < 20, and x is a prime number, then which of the following represents the list form of the set of such numbers?

Solution:
Given:
x ∈ N and 10 < x < 20

List all natural numbers between 10 and 20
⇒ 11, 12, 13, 14, 15, 16, 17, 18, 19

Identify the prime numbers among them
⇒ 11 → prime.
⇒ 12 → divisible by 2; not prime.
⇒ 13 → prime.
⇒ 14 → divisible by 2; not prime.
⇒ 15 → divisible by 3 and 5; not prime.
⇒ 16 → divisible by 2; not prime.
⇒ 17 → prime.
⇒ 18 → divisible by 2 and 3; not prime.
⇒ 19 → prime.

∴ List of prime numbers in this range
{11, 13, 17, 19}