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Question
Which statement below is true?(1 point)
Responses

All Prime Numbers are odd.
All Prime Numbers are odd.

2 is a Composite Number.
2 is a Composite Number.

2 is the only even number that is Prime.
2 is the only even number that is Prime.

All Composite Numbers are even.
All Composite Numbers are even.
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explain but explain in a way I could write it or draw it on paper

Answer 1

Answer: "2 is the only even number that is Prime." (the third statement) — here's how to show it on paper.

1) Definition (write it down):
- Prime: a number >1 whose only positive divisors are 1 and itself.
- Composite: a number >1 that has at least one divisor besides 1 and itself.

2) Show 2 is prime (write this):
- Divisors of 2: 1 and 2. So it has exactly two divisors → 2 is prime.

3) Show every other even number is composite (write & draw):
- Take any even number n > 2. By definition n = 2·k for some integer k ≥ 2.
- So n has divisors 1, 2, and n (at least). Since it has a divisor 2 different from 1 and itself, it is composite.
- Example on paper: list 4 = 2·2 (divisors 1,2,4) so composite; 6 = 2·3 (1,2,3,6) composite; 8 = 2·4 (1,2,4,8) composite. Draw arrows from each number to its divisors to make it clear.

4) Use counterexamples to reject the other statements (write these):
- "All prime numbers are odd." — False because 2 is prime but even. Write primes: 2, 3, 5, 7, 11… circle 2 and note it’s even.
- "2 is a composite number." — False because we showed its only divisors are 1 and 2.
- "All composite numbers are even." — False: give an odd composite example, e.g. 9 = 3·3 (divisors 1,3,9) or 15 = 3·5. Draw arrows for 9 to 1,3,9 to show it’s composite but odd.

That demonstrates why the correct statement is: 2 is the only even prime.