Which of the following statements are so related that they cannot both be true, nor can they both be false?

A. All dogs are omnivores
B. Some dogs are omnivores
C. Some dogs are not omnivores
D. No dogs are omnivores

Choose the correct answer from the options given below:

Correct option is A

If C is true, then not all dogs are omnivores, which directly contradicts A (which claims that all dogs are omnivores).

Therefore, A and C cannot both be true, and they cannot both be false. If one is true, the other must be false, and vice versa.

Information Booster:

1. Contradictory statements cannot be true at the same time, nor can they both be false at the same time.

2. In the square of opposition, contradictory pairs are in direct opposition to each other.

3. Statements like "All dogs are omnivores" and "Some dogs are not omnivores" cannot coexist logically.

4. Contradictories create a logical boundary for any truth-value assessment, ensuring clarity in reasoning.