Which of the following propositions are contrary to each other?

A) All fishes are mammals.

B) Some fishes are mammals.

C) No fishes are mammals.

D) Some fishes are not mammals.

Choose the correct answer from the options given below:

The correct answer is A and C Only.

To understand why this is the correct answer, we can refer to the traditional Square of Opposition in categorical logic, which defines the relationships between different types of categorical propositions.

There are four standard types of categorical propositions:
1. A proposition (Universal Affirmative): "All S is P." (Statement A: "All fishes are mammals.")
2. E proposition (Universal Negative): "No S is P." (Statement C: "No fishes are mammals.")
3. I proposition (Particular Affirmative): "Some S is P." (Statement B: "Some fishes are mammals.")
4. O proposition (Particular Negative): "Some S is not P." (Statement D: "Some fishes are not mammals.")

In the Square of Opposition, the relationship of contraries exists between the two universal propositions, which are the A and E propositions.
Contrary propositions have the following logical properties:
- They cannot both be true at the same time.
- However, they can both be false at the same time.

In this problem, Statement A ("All fishes are mammals") and Statement C ("No fishes are mammals") represent the A and E propositions. Because they are the universal affirmative and universal negative statements on the same subject and predicate, they are contrary to each other. Therefore, A and C Only is the correct choice.