Which of the following statements is true ?

Question

Accepted Answer

Option 1 states that "1 is not a prime number," and this is indeed the correct statement. Let's delve into the reasoning behind this and why the other options are incorrect.

1. **Explanation for Option 1:**
   - A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number must have exactly two distinct positive divisors.
   - The number 1 only has one positive divisor, which is itself. Therefore, it does not meet the criteria of having exactly two distinct positive divisors.
   - As a result, 1 is not considered a prime number, making Option 1 the correct statement.

2. **Explanation for why Option 2 is incorrect:**
   - Option 2 claims that "1 is a prime number." As explained above, a prime number must have exactly two distinct positive divisors. Since 1 only has one divisor (itself), it does not qualify as a prime number. Therefore, Option 2 is incorrect.

3. **Explanation for why Option 3 is incorrect:**
   - Option 3 states that "1 is a composite number." A composite number is defined as a natural number greater than 1 that has more than two positive divisors. Since 1 only has one divisor, it does not meet the criteria for being a composite number. Hence, Option 3 is incorrect.

4. **Explanation for why Option 4 is incorrect:**
   - Option 4 claims that "2 is not a prime number." However, 2 is the smallest and the only even prime number. It has exactly two distinct positive divisors: 1 and 2 itself. Therefore, 2 is indeed a prime number, making Option 4 incorrect.

In conclusion, Option 1 is the correct statement because it accurately reflects the mathematical definition of a prime number, and 1 does not meet the criteria to be classified as such.