Question 1 Which of the following is a correct disproof of t

Question 1

Which of the following is a correct disproof of the claim \"All prime numbers are odd.\"

9 is odd but it is not a prime number

The definition is prime number is a number that is only divisible by 1 and itself. There is nothing in the definition that says it has to be odd. Therefore, prime numbers don\'t have to be odd.

The definition of \"odd\" is that the number can be written as 2k+1 for some integer k. If only odd numbers could be primes, then there could never be two adjacent prime numbers. Since there are infinitely many primes, it must be that at least some of them must be adjacent. QED by contradiction.

9 is odd but it is not a prime number

2 is a prime number and 2 is even

The claim cannot be disproven -- it\'s true! If a number is not odd, it is even, which means it is divisible by 2, which means it is not prime. QED.

Question 3

Suppose you are working through the steps of the 3x+1 conjecture, and at a certain step end up with a value of 30. If you continue to apply the instructions of the 3x+1 conjecture, what value would you reach after completing two more steps?

	Which of the following is a correct disproof of the claim \"All prime numbers are odd.\"
Selected Answer: 9 is odd but it is not a prime number Answers: The definition is prime number is a number that is only divisible by 1 and itself. There is nothing in the definition that says it has to be odd. Therefore, prime numbers don\'t have to be odd. The definition of \"odd\" is that the number can be written as 2k+1 for some integer k. If only odd numbers could be primes, then there could never be two adjacent prime numbers. Since there are infinitely many primes, it must be that at least some of them must be adjacent. QED by contradiction. 9 is odd but it is not a prime number 2 is a prime number and 2 is even The claim cannot be disproven -- it\'s true! If a number is not odd, it is even, which means it is divisible by 2, which means it is not prime. QED.

Solution

Solution 1:

disproof of the claim \"All prime numbers are odd.\"

number 2 is a prime number but it is not an odd number hence a disproof...