Set A = x ∈ N : 13 < x < 17 and x is a prime number. Find the number of elements in the power set of A.

The set $A$ is defined as $A = \{x \in N: 13 < x < 17 \text{ এবং } x \text{ মৌলিক সংখ্যা}\}$.
This means $x$ must be a natural number greater than 13 and less than 17, and $x$ must be a prime number.
The natural numbers between 13 and 17 are 14, 15, 16.

• 14 is not a prime number ($14 = 2 \times 7$).
• 15 is not a prime number ($15 = 3 \times 5$).
• 16 is not a prime number ($16 = 2 \times 8$). Since there are no prime numbers between 13 and 17, the set $A$ is an empty set.

$$A = \{\}$$

The number of elements in $A$, denoted as $|A|$, is 0.

$$|A| = 0$$

The number of elements in the power set of a set with $n$ elements is given by the formula $2^n$.
In this case, $n = |A| = 0$.
So, the number of elements in the power set of $A$, denoted as $|P(A)|$, is $2^0$.

$$|P(A)| = 2^0 = 1$$

The calculated number of elements in $P(A)$ is 1.
Comparing this with the given options:
ক) 0
খ) 1
গ) 4
ঘ) 8
The correct option is খ).

The number of elements in $P(A)$ is $\boxed{\text{1}}$.