p-: There exists a natural number which is prime. Statement p can be interpreted as

Options

A. Every natural number is prime number
B. There is at least one natural number which is prime
C. There is at most one natural number which is prime
D. Every prime number is a natural numbers

Answer

To interpret the statement \( p \): "There exists a natural number which is prime," we can analyze it step by step.

### Step-by-Step Solution

1. **Understanding the Statement**:
The statement \( p \) asserts that there is at least one natural number that is prime. This means that the existence of a prime number among the natural numbers is being claimed.

2. **Identifying the Meaning of "There Exists"**:
The phrase "there exists" indicates that we are looking for at least one example. In mathematical terms, this is often denoted by the symbol \( \exists \). Hence, we can express the statement as:
\[ \exists n \in \mathbb{N} \text{ such that } n \text{ is prime} \]

3. **Evaluating the Options**:
We need to evaluate the given options based on the interpretation of statement \( p \):
- **Option 1**: "Every natural number is a prime number."
- This is incorrect because not all natural numbers are prime (e.g., 1, 4, 6, etc. are not prime).
- **Option 2**: "There is at least one natural number which is prime."
- This is correct as it directly reflects the meaning of statement \( p \).
- **Option 3**: "There is at most one natural number which is prime."
- This is incorrect because the statement does not limit the number of primes; it only asserts that at least one exists.
- **Option 4**: "Every prime number is a natural number."
- While this is true, it does not directly interpret statement \( p \).

4. **Conclusion**:
The correct interpretation of statement \( p \) is given by **Option 2**: "There is at least one natural number which is prime."