"No fish are mammals. All whales are mammals. Therefore no whales are fish." — Abhay thinks this…
"No fish are mammals. All whales are mammals. Therefore no whales are fish." — Abhay thinks this reasoning is just as broken as the earlier "some A, some B" reasoning. His sister says this particular reasoning is actually valid. Who is right?
Who do you think is right? Pick one.
The answer: His sister is right, "no A are B" plus "all C are B" reliably proves "no C are A"
Why
Abhay noticed that both puzzles use the words 'some'/'no' plus a shared middle category, and reasonably assumed they must all break the same way — but the specific WORDS used in a syllogism (all, some, no) genuinely change whether a pattern is reliable, not just decoration on the sentences. 'No fish are mammals' places fish and mammals in completely separate, non-overlapping groups; 'all whales are mammals' places whales entirely inside the mammal group. Since whales sit fully inside 'mammals', and 'mammals' has zero overlap with 'fish', whales cannot possibly reach into the fish group either — there is no gap for them to slip through. Test it by trying to build a counter-example, the same way the earlier puzzle's furniture-and-trees case was built: try to imagine something that is 'all mammal' and also somehow 'a fish', while fish and mammals never overlap at all — it is not possible to construct one, unlike the furniture case where a real counter-example existed. His sister is right: 'no A are B, all C are B, therefore no C are A' is a genuinely valid pattern — not every syllogism with 'some' or 'no' in it is unreliable; the exact words used change whether the pattern can be trusted.
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