Discussion
How does the placement of a negation relative to a quantifier matter?
Answer: B
Not everything is F means something is not F, and not something is F means everything is not F, so pushing a negation through a quantifier exchanges the two quantifiers. That is the quantifier form of De Morgan's laws and it is what drives negations inward during clausal conversion. Commuting freely, disappearing and being restricted to atoms are all false. A rewriting rule that exchanges one operator for another, rather than merely moving it, is worth stating carefully because the exchange is easy to forget.
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