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Logic - Is this equivalent?

  1. Mar 1, 2009 #1
    Is it equivalent?
    [tex]
    ( \forall x \in S \forall y P(x) ) <=> \neg ( \exists x \in S^{c} \exists y \neg P(x) )
    [/tex]

    Attempt at solution
    I think it should be
    [tex]
    ( \forall x \in S \forall y P(x) ) <=> \neg ( \exists x \in S \exists y \neg P(x) )
    [/tex]
    The diiference to the above statement is [tex]S^{c}[/tex].
     
    Last edited: Mar 1, 2009
  2. jcsd
  3. Mar 1, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Equivalences

    Yes, your statement is correct.
     
  4. Mar 1, 2009 #3
    Re: Equivalences

    Please, can you clarify whether it is the first statement or my attempt at solution?
     
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