**QUESTION TEXT:**** **Which one of the following most accurately…

**QUESTION TYPE:**** **Flawed Reasoning

**CONCLUSION:**** **Laura concludes that Fermat was neither lying nor mistaken when he claimed to have proven the theorem.

**REASONING:**** **Someone else did prove the theorem (therefore it was *possible *to prove the theorem.)

**ANALYSIS:**** **Laura makes the mistake of assuming that since it was *possible *for Fermat to have proven the theorem then Fermat *must have *proven the theorem.

It is possible that Fermat didn’t actually prove the theorem, even though someone else did later.

___________

- The fact that someone did prove the theorem does not
*contradict*the idea that Fermat did. In fact it shows its is*possible*that Fermat did prove it. It doesn’t make it certain that Fermat proved the theorem, of course. - Laura hasn’t said anything about the quality of Fermat’s character.
**CORRECT.**For Fermat to have proven the theorem it is necessary that it was*possible*. But the mere fact that it was possible doesn’t mean that Fermat actually*did*prove the theorem.- Everyone can figure out what provable means: possible to prove true.
- Laura doesn’t mention either of these two phenomena.
*Joseph*made the mistake of thinking that a true claim (the theorem can be proven) was false, but that doesn’t have much to do with Laura’s reasoning.

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