Exercise 1 Page 329

Are the examples given really counterexamples?

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We are asked to find the truth value of the following statement. If two even numbers are multiplied, then the product is an even number. Three of the choices claim that this is false and claim to give a counterexample. Let's investigate these examples. To have a counterexample of a conditional, we need an example where the hypothesis is true, but the conclusion is not. In this case, we need two even numbers with a product that is not even.

Example	Hypothesis	Conclusion	Counterexample?
8* 4=32	True, both 8 and 4 are even.	True, 32 is even.	No, the conclusion is true.
7* 6=42	False, 7 is not even.	True, 42 is even.	No, the conclusion is true.
3* 10=30	False, 3 is not even.	True, 30 is even.	No, the conclusion is true.

None of these are counterexaples, so none of these justify the claim that the statement is false. So answer choices A, B and C are certainly not correct. In fact, the statement is true, and answer D is the correct choice.

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