If the statement "no animals are fishes" is given as false, then which of the following statements can be immediately inferred to be true?

A) All fishes are animals.

B) Some animals are not fishes.

C) All animals are fishes.

D) Some animals are fishes.

Choose the correct answer from the options given below:

The correct option is D Only.

To understand why this is correct, we can analyze the relationships between categorical propositions using the classical Square of Opposition in deductive logic.
Let us define the subject term as "animals" and the predicate term as "fishes".

The statement "No animals are fishes" is a Universal Negative proposition (traditionally denoted as E).
We are given that this E proposition is false.

Let us examine what can be immediately inferred from the falsity of the E proposition:

1. Contradictory Relationship (E and I):
A Universal Negative proposition (E: "No S is P") and a Particular Affirmative proposition (I: "Some S is P") are contradictory to each other. By definition, contradictory statements must have opposite truth values. Since the E statement ("No animals are fishes") is false, its contradictory I statement (D: "Some animals are fishes") must be true. Therefore, statement D is immediately inferred to be true.

2. Contrary Relationship (E and A):
The Universal Affirmative proposition (A: "All S is P", corresponding to statement C: "All animals are fishes") is the contrary of the E proposition. Contraries cannot both be true, but they can both be false. Therefore, if the E proposition is false, the truth value of the A proposition (statement C) is undetermined (it could be either true or false) and cannot be immediately inferred.

3. Subaltern Relationship (E and O):
The Particular Negative proposition (O: "Some S is not P", corresponding to statement B: "Some animals are not fishes") is the subaltern of the E proposition. Under the rules of subalternation, the falsity of the universal proposition does not tell us anything about the truth value of the particular proposition. Thus, if E is false, the truth value of O (statement B) is undetermined.

4. Statement A ("All fishes are animals"):
This statement changes the terms by placing "fishes" in the subject position and "animals" in the predicate position. There is no immediate valid inference from the falsity of "No animals are fishes" to the truth of "All fishes are animals".

Consequently, only statement D ("Some animals are fishes") can be immediately and definitely inferred to be true. Thus, the correct option is D Only.