In a square of opposition, if 'No animals with horns are carnivores' is false,…

Concept

In the traditional square of opposition, contradictory propositions always have opposite truth values. Contraries cannot both be true, but they may both be false. In subalternation, truth descends from a universal proposition to its particular subaltern, while falsity ascends from a particular proposition to its universal superaltern.

Application

1. Represent the categorical statements as E: “No horned animals are carnivores,” I: “Some horned animals are carnivores,” A: “All horned animals are carnivores,” and O: “Some horned animals are not carnivores.”

2. Because E is false, its contradictory I must be true. This establishes statement A in the question.

3. E and A are contraries. The falsity of E does not determine A, so the universal affirmative may be true or false. This establishes the undetermined status described in statement D.

4. O is connected to E by subalternation. That rule derives O from true E, but the given false E cannot determine O; the reverse direction would require O to be false. Therefore statement B is not forced, and statement C is also not forced.

Cross-check

In both models, statement A is true and the universal affirmative in statement D remains undetermined. Therefore the correct code is “A and D only”.