FeiFei逻辑第50题--看不懂正确选项，求教

Questions 49-50

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Laura: Your encyclopedia is out of date.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.

50. Which one of the following most accurately describes a reasoning error in Laura’s argument?

(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.   （C）

(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.

凭感觉做对了题，但是甚至看不明白C选项的意思

请NN给解释一下

不胜感激

看题目和选项一头雾水，你要不说答案是C，我十有八九得做错，看了足有5分钟，试着解释一下：C 的意思应该是：把推出结论需要的东西当作能确保结论的东西，可以理解为把必要条件当作充分条件吗？我从来没有做过类似总结性的东西，所以不知道。放到题目里应该是：要证明Fermat没有撒谎或搞错，仅仅Fermat’s theorem 被证明了是不够的，

To prove that Fermat did not lie, it is necessary to know that the theory is provable,but being provable can not ensure that he told the true. However, Laura came up with the conclusion anyway. Hence, she make the mistake stated in C. 

我的翻译是

她将（1结论存在所必须的条件）和（2要确保结论存在所需的充分条件）相混淆了。

mistake(1)for(2)