Which of the following propositions are so related that if one of them is true, the other has to be false and vice-versa?

A) All camels are herbivorous.

B) Some camels are herbivorous.

C) Some camels are not herbivorous.

D) No Camels are herbivorous.

Choose the correct answer from the options given below:

The correct answer is B and D only.

To understand why this is the correct choice, we can analyze the relationship between the propositions using the classical Square of Opposition in categorical logic. Let's first identify the type of each proposition given in the question:
A) "All camels are herbivorous." - This is a Universal Affirmative (A-type) proposition.
B) "Some camels are herbivorous." - This is a Particular Affirmative (I-type) proposition.
C) "Some camels are not herbivorous." - This is a Particular Negative (O-type) proposition.
D) "No camels are herbivorous." - This is a Universal Negative (E-type) proposition.

The question asks for two propositions that are so related that if one is true, the other must be false, and vice-versa. In formal logic, this relationship is known as a contradictory relationship. Contradictory propositions always have opposite truth values; they cannot both be true, and they cannot both be false at the same time.

Under the Square of Opposition, contradictory relationships exist diagonally between:
1. The Universal Affirmative (A) and the Particular Negative (O) propositions (i.e., A and C).
2. The Particular Affirmative (I) and the Universal Negative (E) propositions (i.e., B and D).

Let's evaluate the relationship between B ("Some camels are herbivorous") and D ("No camels are herbivorous"):
- If B is true ("Some camels are herbivorous" is true, meaning at least one camel is herbivorous), then D ("No camels are herbivorous") must be false.
- If B is false (meaning it is not the case that some camels are herbivorous, i.e., zero camels are herbivorous), then D ("No camels are herbivorous") must be true.
- Similarly, if D is true, B must be false; and if D is false, B must be true.

Since the propositions B and D are contradictories, they satisfy the condition that if one is true, the other must be false and vice-versa. Therefore, the correct option is "B and D only".