Which of the following propositions cannot both be false, though they can both be true?
A. All cows are herbivores. B. No cows are herbivores. C. Some cows are herbivores. D. Some cows are not herbivores.
Choose the correct answer from the options given below:

Correct option is B

The propositions C and D are sub-contraries, meaning they cannot both be false at the same time, though they can both be true.
· C. Some cows are herbivores: This is a particular affirmative statement.
· D. Some cows are not herbivores: This is a particular negative statement.
· Sub-contrary propositions (like C and D) cannot both be false but can both be true. If one is false, the other must be true. For example:
· If it were false that "Some cows are herbivores" (C), it would imply that "No cows are herbivores," contradicting D.
· Conversely, if it were false that "Some cows are not herbivores" (D), it would imply that "All cows are herbivores," contradicting C.
Information booster:
· A and D and B and C involve universal and particular statements that do not satisfy the sub-contrary relationship.
· A and C are not logically connected in a way that prevents both from being false.
· Sub-contrary propositions are specific to particular affirmatives and negatives. They maintain that both cannot be false simultaneously.
· In Aristotelian logic, sub-contraries allow particular statements to co-exist truthfully.