Statements: No door is dog. All the dogs are cats. Conclusions: No door is…

Concept: Whether a conclusion follows is decided by checking every diagram (Venn arrangement) consistent with the given statements — a conclusion follows only if it holds in ALL such diagrams. Two established facts matter here. First, a universal negative statement ('No A is B') always converts to 'No B is A' — but conversion only restates a relationship that is ALREADY given between two terms; it cannot manufacture a negative relationship between two terms the premises never directly relate (here, door and cat are linked only through dog, and no valid rule forces a direct door–cat relationship from the two premises). Second, a universal affirmative statement ('All A are B') converts, by limitation, only to 'Some B are A' — it can never be strengthened to 'All B are A' unless a separate premise says so.

1. 'All the dogs are cats' places the entire dog circle inside the cat circle. By conversion-by-limitation, this alone guarantees 'some cats are dogs' in every valid diagram.

2. 'No door is dog' only keeps the door circle away from the dog circle; it does not fix how the door circle relates to the wider cat circle, so more than one diagram remains consistent with both statements.

3. Both consistent diagrams are drawn below: one where the door circle sits fully outside the cat circle, and one where the door circle overlaps the part of the cat circle that lies outside the dog subset.

Cross-check against both diagrams: the dog-inside-cat overlap holds in both, so 'some cats are dogs' is guaranteed regardless of where the door circle sits. The door-cat relationship, however, differs between the two diagrams, so no fixed statement about door and cat is forced in every case. Reversing 'all the dogs are cats' into 'all the cats are dogs' would also require strengthening a 'some' relationship into an 'all' relationship, which conversion never licenses.

Only the conclusion that the dog-cat overlap guarantees — 'some cats are dogs' — holds in every diagram consistent with both statements.