Discussion
What is wrong with writing some student is diligent using implication?
Answer: A
Writing there exists x such that x is a student implies x is diligent is made true by any object that is not a student, since a false antecedent makes the implication true, so the sentence says almost nothing. The formula is satisfied in a domain containing a single stone. Recognising vacuous satisfaction as the mechanism of the error connects it to the same phenomenon in universal restrictions in description logics.
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