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I was given the sentence:

There is at least one person on earth who does not know logic

and was tasked to negate the sentence. I understand from class that existential quantifications become universal quantifications when negated.

My thinking:

The there is at least one person must become either everyone or nobody due to the aforementioned requirement of quantification negation.

However, examples in class have now confused me as to the desirable sentence structure of a negated predicate. Thus, I have four possibilities for the most accurate negation of the existential quantification:

  1. Nobody on earth does not know logic

  2. Everyone on earth knows logic

  3. Nobody on earth knows logic

  4. Everyone on earth does not know logic

Which sentence would you deem the most correct when negating the original predicate and why?

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    $\begingroup$ The original sentence is true iff there is a person on earth who doesn't know logic. $$$$ To make it false, there must not be a person on earth who doesn't know logic: i.e., every person on earth does know logic. $$$$ That is possibility (2). $\endgroup$ – Benjamin Dickman Jan 25 '18 at 4:02
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I like (2), just based on the meaning of the original sentence...

(3) and (4) are definitely out...

(1) appears to be ok too, as long as you don't allow neither knowing or not knowing logic... this reduces to neither $a$ nor $-a$, which i believe is known as the law of excluded middle...

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According to my professor the correct negation is everyone on earth knows logic

Option 2 is most correct negation

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