[求助]LSAT题目中的逻辑关系

No senator spoke at the convention unless he or she was a Democrat. No Democrat both spoke at the convention and was a senator.Which one of the following conclusions can be correctly drawn from the statements above?
(A) N one but senators spoke at the convention.
(B) No Democrat spoke at the convention.
(C) Only Democrats spoke at the convention.
(D) No senator spoke at the convention.
(E) Some Democrat senators spoke at the convention.

My understanding: A--->senator; B--->spoke at the convention; C---a Democrat, so reasoning will be:

A&B--->C, not C---> A&B, how is possible? Thanks in advance~

果然厉害,这么一说我就明白了,谢谢版主~~最近逻辑陷入瓶颈,努力突破中...