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Negation

 
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Mar1-05, 12:39 AM   #1
 

Negation

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]
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Mar1-05, 12:49 AM   #2
AKG
 
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looks right
Mar1-05, 01:46 AM   #3
 
Quote by gnome
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]
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).
Mar1-05, 11:08 PM   #4
 

Negation

Thanks guys.
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