Understanding the Logical Inference

The question asks us to determine which statements are necessarily true if the premise "No birds are animals" is considered false.

Analyzing the Core Statement

The initial statement is: "No birds are animals."

Let's represent the set of all birds as 'B' and the set of all animals as 'A'. The statement "No birds are animals" means that the intersection of these two sets is empty. Mathematically, this is $B \cap A = \emptyset$. This implies that there is no overlap between the group of birds and the group of animals; no member of set B is also a member of set A.

Implication of the Statement Being False

We are told that the statement "No birds are animals" is false. The logical negation (opposite) of "No A are B" is "Some A are B".

Therefore, if "No birds are animals" is false, it directly implies that the statement "Some birds are animals" must be true. This means there exists at least one entity that is both a bird and an animal. In set notation, this is $B \cap A \neq \emptyset$.

Evaluating the Options Based on the True Implication

We now need to check which of the options (A, B, C, D) are necessarily true, given that "Some birds are animals" is true.

Option D: "Some birds are animals."

As we deduced, this is the direct logical consequence of the original statement being false. Therefore, statement D is true.

Option C: "Some animals are birds."

This statement means there exists at least one animal that is also a bird. If we know that "Some birds are animals" is true, it means there's at least one creature that belongs to both categories. Let's call this creature 'X'. Since X is a bird and X is an animal, it logically follows that there exists an animal (namely X) that is a bird. Thus, "Some animals are birds" is also true. Statements C and D are logically equivalent.

Option A: "Some animals are not birds."

This statement claims there is at least one animal that does not belong to the bird category. While this might be true in the real world, it doesn't *necessarily* follow from "Some birds are animals". Consider a hypothetical scenario where every animal in existence is also a bird, and every bird is also an animal. In this specific case, "Some birds are animals" is true, but "Some animals are not birds" would be false (because all animals *are* birds). Since we found a case where A is false while the premise holds, Option A is not necessarily true.

Option B: "Some birds are not animals."

This statement claims there is at least one bird that does not belong to the animal category. Similar to Option A, this doesn't necessarily follow. Using the same hypothetical scenario where all birds are animals and all animals are birds, "Some birds are animals" holds true, but "Some birds are not animals" would be false (because all birds *are* animals). Therefore, Option B is not necessarily true.

Conclusion

Based on the logical analysis, if the statement "No birds are animals" is false, the only statements that must be true are "Some birds are animals" (D) and "Some animals are birds" (C).

Therefore, the correct choice includes options C and D only.