Which of the following statements are so related that they cannot both be false, although they can both be true?
A. Some professors are spiritualists.
B. All professors are spiritualists.
C. No professors are spiritualists.
D. Some professors are not spiritualists.
Choose the correct answer from the option below:

Correct option is C

A and D only are the statements that are related in such a way that they cannot both be false, though they can both be true. Statement A ("Some professors are spiritualists") implies that there is at least one professor who is a spiritualist. Statement D ("Some professors are not spiritualists") implies that there is at least one professor who is not a spiritualist. Both statements can be true if the group of professors is diverse—some being spiritualists and some not. However, they cannot both be false because if no professors were spiritualists, it would contradict the possibility of some being spiritualists, and if all professors were spiritualists, it would contradict the possibility of some not being spiritualists.
Information Booster:
(B) "All professors are spiritualists" and (C) "No professors are spiritualists" cannot both be true at the same time and are logically exclusive (i.e., if one is true, the other must be false), making them unable to fulfill the condition where both can be true.
(A) and (C) cannot both be true because if some professors are spiritualists (A), then it cannot be true that no professors are spiritualists (C).