费费逻辑63题请教

Some good cooks are gourmet cooks who pride themselves on always using extravagantly rich ingredients in elaborate recipes. Some good cooks can be characterized as fast-food cooks. They may use rich ingredients as long as the recipes are easy to follow and take little time. Other good cooks are health food enthusiasts, who are concerned primarily with the nutritional value of food. But even though not all good cooks are big eaters, they all enjoy preparing and serving food.

If the information in the passage is true, which one of the following CANNOT be true?

(A) Most good cooks do not use extravagantly rich ingredients.

(B) Everyone who enjoys preparing and serving food is a good cook.

(C) More good cooks who use extravagantly rich ingredients are big eaters than are good cooks who do not use such ingredients.

(D) There are fewer good cooks who enjoy serving and preparing food than there are good cooks who are big eaters.

(E) Gourmet cooks, fast-food cooks, and cooks who are health food enthusiasts are all big eaters.

答案是D。我的问题是为什么B和E就是can be true，于是就不对了

原文先说了三种good cooks及其各自爱好，结论说"就算这些good cooks不都是大胃王，他们都喜欢做饭"

解答版的解释中说"B.
                    从结论可以推出。E是从原文推出"

但是B是怎么从结论推得呢？

E我怎么觉得和原文是反着的呢？原文说是good cooks的GC, FFC 和HFC不都是大胃王，good cooks是所有GC, FFC和HFC的子集，子集不都是大胃王，全集——所有的GC, FFC和HFC怎么能全是大胃王呢，那么E不就是cann't be true了吗？

想不明白啊，那位NN帮助一下，多谢拉