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.
“All that glitters is not gold” → “There exists an object that glitters and is not gold”.
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,
they can not swim and not sink.
That sounds like a caveman. ↩