Which of the following statements are so related that they cannot both be false, though they can both be true?

A. Some saints are materialists.

B. All saints are materialists.

C. No saints are materialists.

D. Some saints are not materialists.

Choose the correct answer from the options given below: 

the correct answer is A and D only.

Important Points 

Statement A: Some saints are materialists.
Statement B: All saints are materialists.
Statement C: No saints are materialists.

Statement D: Some saints are not materialists.

First, let's consider statements A and B:

• If statement A is true, it implies that there are saints who are materialists.
• If statement B is true, it implies that every single saint is a materialist.

Since statement A allows for the possibility of some saints being materialists (without requiring all saints to be materialists), it is not contradictory to statement B.

Therefore, statements A and B can both be true.

Next, let's consider statements C and D:

• If statement C is true, it means there are no saints who are materialists.
• If statement D is true, it means there are saints who are not materialists.

If statement C is true, it contradicts statement D because statement D implies the existence of saints who are not materialists. Therefore, statements C and D cannot both be true.

• Based on this analysis, we can conclude that
• statements A (Some saints are materialists) and
• B (All saints are materialists) can both be true,
• while statements C (No saints are materialists) and D (Some saints are not materialists) cannot both be true.

Thus, the correct answer is option 2) A ad D only.

 Additional Information