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Thread: Help... proving arguments.!!!

  1. #1
    Nov 2007

    Help... proving arguments.!!!


    I have a problem regarding arguments. When we are asked to prove whether an argument is valid or not... is there a specific way that you should follow to solve the question...???

    Example.. like lets say.. this argument.

    P ---------> R
    (not) P ----> Q
    Q ---------> S
    then (not) R -----> S (the conclusion).

    Basically... is there a way or some kind of a hint to find if the argumet is valid or not without trying to solve the argument...??? I hope this doesnt sound absured.. because basically most of the time I get lost trying to derive the conclusion and ending up assuming that the argument in not valid then it turn out that its in fact valid or vice versa.

    Any help would be appreciated. Thanks.
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  2. #2
    Super Member

    May 2006
    Lexington, MA (USA)
    Hello, MMM88!

    . . . $\displaystyle P \to R$
    . .$\displaystyle \sim\! P \to Q$
    . . . $\displaystyle Q \to S$
    . . .$\displaystyle - - - -$
    $\displaystyle \therefore\;\sim\! R \to S$

    Look at the conclusion: .$\displaystyle \sim\! R \to S$

    Do we have a "chain" of implications that will produce that conclusion?

    Well, no . . . nothing starts with $\displaystyle \sim\! R$

    But wait . . . the contrapositive of the first statement is: .$\displaystyle \sim\! R \to\: \sim\!P$

    So we have:

    . .$\displaystyle \sim\!R \to \sim\!P \;\;\;\text{Contrapositive}$
    . .$\displaystyle \sim\! P \to Q \quad\;\; \text{Given}$
    . . .$\displaystyle Q \to S \qquad \text{Given}$
    . . .$\displaystyle - - - -$
    $\displaystyle \therefore\;\sim\!R \to S \qquad \text{Law of Syllogism}$

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