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Suppose $x \notin A$. If I were to rewrite using negation symbol $\lnot$, which one is true?

  1. $x \lnot \in A$
  2. $x \in \lnot A$

I'm guessing the first, because the second assumes $x$ does belong somewhere else (specifically $A^c$), but this assumption did not exist in original statement $x \notin A$.

MinYoung Kim
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1 Answers1

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I think neither of these two.

The correct answer should be $ \lnot (x \in A) $.

peter.petrov
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  • ok but what's wrong with 1? Is it just convention that we don't do $\lnot \in$ ? – MinYoung Kim Sep 28 '19 at 22:14
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    Normally you apply the negation symbol to some boolean/logical statement. If you write 1. it looks as if you are applying the negation symbol to the 'belongs to' symbol which does not make sense (to me at least). So I form the whole logical statement $ x \in A $ then I apply the negation symbol to it. – peter.petrov Sep 28 '19 at 22:18