Question

dana says that all even numbers are composite. is she correct? yes, because all even numbers have a factor of 2. yes, because all odd numbers are prime. no, because the number 2 is even but is also prime. no, because the number 9 is odd but is also composite.

Explanation:

To determine if Dana is correct, we recall the definitions: A prime number has exactly two distinct positive divisors (1 and itself), and a composite number has more than two distinct positive divisors. The number 2 is even. Its divisors are 1 and 2, so it is prime (not composite). This shows not all even numbers are composite. Let's analyze each option:

• First option: Incorrect. Having a factor of 2 doesn't make all even numbers composite (e.g., 2 is even and prime).
• Second option: Incorrect. Not all odd numbers are prime (e.g., 9 is odd and composite), and this is irrelevant to even numbers.
• Third option: Correct. 2 is even and prime, so not all even numbers are composite.
• Fourth option: Incorrect. This is about an odd number (9) being composite, which doesn't address if all even numbers are composite.

Answer:

C. No, because the number 2 is even but is also prime. (Note: Assuming the third option with the text "No, because the number 2 is even but is also prime." is labeled as, say, C. If the original options had labels like A, B, C, D, we use the correct label with the text. From the image, the third option (bottom left) is the correct one, so if we assume labels: Let's say the options are A (top left), B (top right), C (bottom left), D (bottom right). Then the answer is C. No, because the number 2 is even but is also prime.