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Are the examples given really counterexamples?
D
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.