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Thread: Symbolic Logic Proof Help

  1. #1
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    Symbolic Logic Proof Help

    1. (P⋅G) ⊃ R
    2. (R⋅S) ⊃ T
    3. P⋅S
    4. G v R

    The conclusion is R v T.

    I don't even know where to start and I can use basic rules of inference (MT, Disjunctive Syllogism, Dilemma, etc.) and replacement rules (Contraposition, Commutation, etc.).

    Any help would be appreciated!
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  2. #2
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    Quote Originally Posted by joejoejohnson View Post
    1. (P⋅G) ⊃ R
    2. (R⋅S) ⊃ T
    3. P⋅S
    4. G v R
    The conclusion is R v T.
    I would prove this by contradiction.
    Suppose it is not true.
    $\displaystyle \begin{gathered}
    5.\neg R \cdot \neg T \hfill \\
    6.\neg P \vee \neg G,\,1 \hfill \\
    7.\neg R \vee \neg S,\,2 \hfill \\
    8.\neg R,\,5 \hfill \\
    9.G,\,4,8 \hfill \\
    10.\neg \neg G,\,9 \hfill \\
    11.\neg P,\,6,10 \hfill \\
    12.P,\,3 \hfill \\
    13.P \cdot \neg P,\,12,11 \hfill \\
    \end{gathered} $
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