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Thread: cant solve this problem (proof by contradiction)

  1. #1
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    cant solve this problem (proof by contradiction)

    i tried to solve this question 100 times but could n't get the right answer
    plz help guys
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  2. #2
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    $\displaystyle \begin{array}{llr}
    1 & {\left( {S \wedge R} \right) \to Q} & {} \\
    2 & {\neg R \to \neg P} & {} \\
    3 & {S \wedge P} & {} \\
    4 & {\neg Q} & {\text{assume}} \\

    \end{array}$
    $\displaystyle
    \begin{array}{llr}
    5 & {\neg \left( {S \wedge R} \right)} & {1,4} \\
    6 & {\neg S \vee \neg R} & 5 \\
    7 & S & 3 \\
    8 & {\neg R} & 6 \\
    9 & {\neg P} & {2,8} \\
    {10} & P & 3 \\
    {} & {P \wedge \neg P} & {8,9 \text{ contradiction}} \\ \end{array} $
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