B VS. C

Let's look at (B) and (C). (B) says, "It mistakenly assumes that the quality of a person's character can legitimately be taken to guarantee the accuracy of the claims that person has made." The problem with (B) is that she says that Joseph is wrong about a particular claim, but this doesn't mean that she's basing her conclusion on undermining one of his claims. She's not relying on the quality of Fermat or Joseph's character to arrive at her conclusion, so this is out. (C) says, "It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows." (C) is great because it's necessary for her conclusion (which is that Fermat is right) that the theorem is provable. But it's not sufficient to ensure that conclusion, so this is why (C) is correct. Let us know if you have any other questions!

Hello, I didn't choose C because there was no sufficient and necessary language in her argument. I still don't understand why C is correct instead of E. Can someone explain further please?

Hi Abigail! Not an instructor but I think I might be able to shed some light... If F was not lying/mistaken about proving his theorem (that is, if F proved his theorem), then it must the the case that his theorem is provable. (After all, if something is proved, it's provable.) But merely that the theorem is provable does not ensure that F actually proved it and proved it correctly. Likewise, just because Laura can demonstrate that the theorem is provable does mean Laura can conclude that F actually proved the theorem. Laura, by doing so, commits the classic S&N flaw: asserting a necessary condition (theorem is probable) to conclude a sufficient (F proved it) or reversing without negating.