Problem:
Consider the statement, "If is not prime, then is prime." Which of the following values of is a counterexample to this statement?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
An implication is false if and only if the hypothesis is true but the conclusion is false. Choice , is a counterexample to the statement because the hypothesis is true ( is not prime) but the conclusion is false is not prime). For answer choices and , is prime, so the hypothesis is false and these values of do not provide a counterexample. For choices , , and , is prime, so the conclusion is true and these values of do not provide a counterexample.
The problems on this page are the property of the MAA's American Mathematics Competitions