Discussion
How is the claim that a student passed correctly denied?
Answer: D
Denying an existential claim requires that no instance exists at all, so the negation is that every student failed. The second and third options are the negation of the universal claim rather than of this one. Working through the four combinations of quantifier and negation once, and writing each in symbols, converts a persistent source of confusion into a mechanical rewriting rule that can be applied without thought.
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