This is trivial but kind of fun.
In my old analysis textbook, there was a problem to take old idioms and turn them into logical statements.
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“All that glitters is not gold” → “There exists an object that glitters and is not gold”.
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What makes the following sentence ambiguous: “a death row prisoner can’t have too much hope” → can’t could mean “can’t hope too much” or “shouldn’t hope too much”.
There was also one on negating implications.
“They will sink unless they swim”. In logic1: if not swim then sink.
A simple definitional shift makes finding the negation trivial.
A handy identity is \(p \implies q \equiv \neg p \lor q\). The negation
of that is \(p \land \neg q\). By rewriting the idiom as a disjunction,
we get they can not swim and not sink.
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That sounds like a caveman. ↩