Form a valid conclusion, using all the statements for each argument. Give reasons.
If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number.
N is not a prime number.
A) N is not greater than 2.
B) N is an even number.
C) 2 does not divide a positive integer N and N is not greater than 2.
D) 2 does not divide a positive integer N or N is not greater than 2.
E) none of these

Question

Form a valid conclusion, using all the statements for each argument. Give reasons. ​
If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number.
N is not a prime number.
A) N is not greater than 2.
B) N is an even number.
C) 2 does not divide a positive integer N and N is not greater than 2.
D) 2 does not divide a positive integer N or N is not greater than 2.
E) none of these

Quizplus · Accepted Answer

Given that if 2 divides a positive integer N and N is greater than 2, then N is not a prime number. The conclusion that N is not a prime number does not necessarily mean that both conditions (2 divides N and N is greater than 2) are false. It means at least one of the conditions for N being a prime number is not met. Therefore, the correct conclusion is that either 2 does not divide N or N is not greater than 2, which matches option D.

Form a Valid Conclusion, Using All the Statements for Each