If A={x:x `in` N and x is an odd prime number less than 17}, then the cardinal number of A is

Options

A. 8
B. 6
C. 5
D. none of these

Answer

To solve the problem, we need to find the set A defined as follows:

**Step 1: Identify the set A.**
Set A is defined as:
\[ A = \{ x : x \in \mathbb{N} \text{ and } x \text{ is an odd prime number less than 17} \} \]

**Step 2: List the prime numbers less than 17.**
The prime numbers less than 17 are:
\[ 2, 3, 5, 7, 11, 13, 17 \]

**Step 3: Filter the odd prime numbers from the list.**
From the list of prime numbers, we need to select only the odd ones:
- The prime numbers are: 2, 3, 5, 7, 11, 13
- The odd prime numbers are: 3, 5, 7, 11, 13

**Step 4: Count the odd prime numbers.**
Now, we count the odd prime numbers we have identified:
- The odd prime numbers are: 3, 5, 7, 11, 13
- There are 5 odd prime numbers.

**Step 5: Determine the cardinal number of set A.**
The cardinal number (the number of elements) of set A is:
\[ |A| = 5 \]

Thus, the answer is:
**The cardinal number of A is 5.**

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