If the statement “Some birds are not mammals” is true, which of the following…

CONCEPT

In the traditional square of opposition, an A-proposition (“All S are P”) and the corresponding O-proposition (“Some S are not P”) are contradictories.

Contradictories cannot both be true and cannot both be false. Therefore, if one is true, the other must be false.

APPLICATION

1. Let B be the set of birds and M the set of mammals.

2. The given statement says that there exists at least one object x such that x belongs to B but not to M: x ∈ B \ M.

3. “All birds are mammals” says B ⊆ M, which would make B \ M empty.

4. The witness x in B \ M directly contradicts B ⊆ M, so “All birds are mammals” must be false.

CONTRAST

• “Some mammals are not birds” concerns M \ B, a region not fixed by the premise.

• “Some birds are mammals” concerns B ∩ M; that region may be populated even when B \ M is also populated.

• “No birds are mammals” makes B ∩ M empty and is compatible with the premise’s witness in B \ M.

CROSS-CHECK

On a Venn diagram, place the given witness inside B but outside M. This single point makes it impossible for the whole of B to lie inside M.

Therefore, the statement that can be immediately inferred to be false is “All birds are mammals.”