Which of the following statements are true regarding contrary propositions?
(A) They cannot both be true (B) They cannot both be false (C) They can both be false (D) If one is true the other must be false
Choose the correct answer from the options given below:

Correct option is C

Contrary propositions are pairs of universal statements (one affirmative and one negative) that have the following properties:
· (A) They cannot both be true: True. In contrary propositions, if one is true, the other must be false. For example, if "All cats are animals" (universal affirmative) is true, then "No cats are animals" (universal negative) must be false.
· (C) They can both be false: True. Contrary propositions can both be false. For instance, both "All cats are animals" and "No cats are animals" can be false if "Some cats are animals" is true.
· (D) If one is true, the other must be false: True. If one of the contrary propositions is true, it necessarily makes the other false, as they are mutually exclusive statements.
· (B) They cannot both be false: This is incorrect for contrary propositions, as contrary propositions can both be false.
Information booster:
1. Contrary propositions involve universal statements that cannot both be true simultaneously, but they can both be false.
2. In Aristotelian logic, contraries are universal in scope and are distinguished from sub-contraries, which are particular.