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Math negation equation

  1. Mar 1, 2005 #1
    I want to negate this: [itex]( \exists x ) ( \forall y ) \Phi (x,y ) [/itex]

    Is this correct?

    [tex]\neg ( ( \exists x ) ( \forall y ) \Phi (x,y ) ) \equiv ( \forall x ) ( \exists y ) \neg \Phi (x,y ) [/tex]
     
  2. jcsd
  3. Mar 1, 2005 #2

    AKG

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    looks right
     
  4. Mar 1, 2005 #3
    Yes.

    ~[(Ex)(Ay)F(x,y)] <-> ~(Ex)(Ay)F(x.y)
    ~(Ex)(Ay)F(x,y) <-> (Ax)~(Ay)F(x,y)
    (Ax)~(Ay)F(x,y) <-> (Ax)(Ey)~F(x,y)
    therefore,
    ~[(Ex)(Ay)F(x,y)] <-> (Ax)(Ey)~F(x,y).
     
  5. Mar 1, 2005 #4
    Thanks guys.
     
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