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Math Help - logic

  1. #1
    Newbie
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    Nov 2008
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    Exclamation logic

    Use the 17 Rules of Inference to prove the following arguments valid.
    Question 1.
    1. (Q . F) v R
    2. (Q v R) > ~P
    3. ~A / ~(A v P)

    Question 2.
    1. A > ~A / ~A

    Question 3.
    1. A > B
    2. C > B / (A v C) > B

    Question 4.
    1. S > R/ S > (R v T)

    ??? Ah
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  2. #2
    Super Member

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    Hello, scoober!

    Here's #3 . . .

    We have the rule: . (p \to q) \;\Longleftrightarrow \;(\sim p \vee q)

    I will call it "ADI" -- Alternate Definition of Implication.


    Use the 17 Rules of Inference to prove the following argument valid.

    3.\;\;\begin{array}{c}A \to B  \\ C \to B \\ \hline (A \vee C) \to B \end{array}

    . . \begin{array}{ccccc} & \text{Statement} && \text{Reason} \\ \hline \\[-3mm]<br />
1. & (A \to B) \wedge (C \to B) & & \text{Given} \\ \\[-3mm]<br />
2. & (\sim A \vee B) \wedge (\sim C \vee B) & & \text{ADI} \\ \\[-3mm]<br />
3. & (\sim A \:\wedge \sim C) \vee B & & \text{Distr.} \\ \\[-3mm]<br />
4. & \sim(A \vee C) \vee B & & \text{DeMorgan} \\ \\[-3mm]<br />
5. & (A \vee C) \to B && \text{ADI}\end{array}

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