Feifei-50

Joseph: My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved. Probably this alleged theorem simply cannot be proved, since---as the article points out---no one else has been able to prove it. Therefore it is likely that Fermat was either lying or else mistaken when he made his claim.

Laura: Your encyclopedia is out of date. Recently someone has in fact proved Fermat’s theorem. And since the theorem is provable, your claim---that Fermat was lying or mistaken---clearly is wrong.

(A) It purports to establish its conclusion by making a claim that, if true, would actually contradict that conclusion.

(B) 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.

(C) It mistakes something that is necessary for its conclusion to follow for something that ensures that the conclusion follows.

(D) It uses the term “provable” without defining it.

(E) It fails to distinguish between a true claim that has mistakenly between believed to be false and a false claim that has mistakenly been believed to be true.

答案是C,应该怎么理解，具体翻译出来是什么意思呢。我看着看着就糊涂了。。。经常混淆楚这种充分必要的关系，期待大家帮我解惑

谢谢Whitney,思路清晰了

哭，还是看不懂。谁再给解释解释？

我相信很多人跟我一样，看不懂C选项在说些什么。句子基本结构：mistake sth.1 for sth.2。 something that is necessary for its conclusion to follow是必要条件的意思；something that
                ensures that the conclusion follows是充分条件的意思。

恩！ 还举一反三！