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Math Help - Determine whether he following logic argument is valid.

  1. #1
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    Determine whether he following logic argument is valid.

    I am stuck in this question. Please help.

    Determine whether he following logic argument is valid.-untitled.jpg
    Last edited by mr fantastic; August 21st 2011 at 12:30 PM. Reason: Re-titled.
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  2. #2
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    Re: Need help in solving this question

    We have to deduce t\rightarrow w, which is equivalent to \neg w \rightarrow \neg t, from:

     \\ \neg p \rightarrow (r \wedge \neg s) \quad (1) \\ t \rightarrow s \quad (2) \\ u \rightarrow \neg p \quad (3) \\ \neg w \quad (4) \\ u \vee w \quad (5) \\ u \quad (6) \mbox{ From 5 and 4} \\ \neg p \quad (7) \mbox{ From 3 and 6 } \\ r \wedge \neg s \quad (8) \mbox{ From 1 and 7 } \\ \neg s \quad (9)\mbox{ From 8 } \\ \neg t \quad (10) \mbox{ From 2 and 9 } \\ \neg w \rightarrow \neg t \quad \mbox{ From 4 and 10 }

    Hence, it's a valid argument. Hope this helps you.
    Last edited by MATHNEM; August 21st 2011 at 12:02 PM. Reason: Corrected negation symbol
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  3. #3
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    Re: Need help in solving this question

    How do you get (9) from 8? Truth table gives F T F F which is something different.
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Need help in solving this question

    Quote Originally Posted by terrorsquid View Post
    How do you get (9) from 8? Truth table gives F T F F which is something different.
    \frac{\alpha  \land \beta}{\alpha }

    and,

    \frac{\alpha  \land \beta}{\beta  }

    Edit:

    Proof:

    \alpha  \land \beta true only when \alpha and \beta are both true. Therefor, if \alpha  \land \beta true at particular reference, so are \alpha and \beta are true in that particular reference.

    And we can write, \alpha  \land \beta \models \alpha and \alpha  \land \beta \models \beta
    Last edited by Also sprach Zarathustra; August 21st 2011 at 02:15 AM.
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    Re: Need help in solving this question

    Quote Originally Posted by Also sprach Zarathustra View Post
    \frac{\alpha  \land \beta}{\alpha }

    and,

    \frac{\alpha  \land \beta}{\beta  }
    Is there somewhere I can read more about that? is it a law of logic? I don't understand.
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  6. #6
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    Re: Need help in solving this question

    Quote Originally Posted by Also sprach Zarathustra View Post
    Proof:

    \alpha  \land \beta true only when \alpha and \beta are both true. Therefor, if \alpha  \land \beta true at particular reference, so are \alpha and \beta are true in that particular reference.

    And we can write, \alpha  \land \beta \models \alpha and \alpha  \land \beta \models \beta
    How do we know that r is true and that s is false though? such that (r\wedge -s) \equiv~ (T\wedge -F)

    Not following sry :S
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  7. #7
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    Re: Need help in solving this question

    We have correctly inferred that r \wedge \sim s is true, but this implies that r is true and so is \sim s.

    Simplification - Wikipedia, the free encyclopedia

    I'm sorry I couldn't find something else.
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  8. #8
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    Re: Need help in solving this question

    A word about not and LaTeX.
    [tex]\neg P[/tex] gives \neg P
    Last edited by mr fantastic; August 21st 2011 at 12:32 PM. Reason: Fixed [tex] and [noparse] tags.
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