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Math Help - First Order Logic : Tableau

  1. #1
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    First Order Logic : Tableau

    This formulae gives me some troubles.

    First Order Logic : Tableau-formulae.png

    Im getting this far before im in trouble:

    First Order Logic : Tableau-formulae2.png

    How do I push the negation inwards ?

    Appreciate all hints or solutions!

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  2. #2
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    Re: First Order Logic : Tableau

    Quote Originally Posted by Razoor View Post
    This formulae gives me some troubles.
    Click image for larger version. 

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    I find your answer puzzling.
    Lets say we are dealing with \mathbb{N} and p(m,n) means m\le n.
    Then (\exists x)(\forall y)[p(x,y)] says "some natural number precedes every natural number". Does that imply that "every natural is preceded by some natural number"?

    Can you use IE, UI, UG & EU in a valid way to get what you need?
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  3. #3
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    Re: First Order Logic : Tableau

    Quote Originally Posted by Plato View Post
    I find your answer puzzling.
    Lets say we are dealing with \mathbb{N} and p(m,n) means m\le n.
    Then (\exists x)(\forall y)[p(x,y)] says "some natural number precedes every natural number". Does that imply that "every natural is preceded by some natural number"?

    Can you use IE, UI, UG & EU in a valid way to get what you need?
    Im not quite sure what you mean with your last question. But this is how i understand the sentence.

    \exists x \forall y p(x,y)

    "There exist an X where all Y is in the same function p(X,Y) which implies that for all Y is there an X in the same function p(X,Y)"

    First of all i need to remove the imply arrow by negating the right side and split up the left and right part like this:

    \exists x \forall y p(x,y) , \neg ( \forall y \exists x p(x,y) )

    You can then remove (\exists x) by introducing a new constant for X.

    \forall y p(A,y) , \neg ( \forall y \exists x p(x,y) )
    Last edited by Razoor; November 5th 2012 at 01:55 AM.
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