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Math Help - [SOLVED] A simple SD logic derivation that is giving me fits

  1. #1
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    [SOLVED] A simple SD logic derivation that is giving me fits

    I need to derive D from the following. Any help would be greatly appreciated

    Premise 1: A & B
    Premise 2: C -> D
    Premise 3: C v ~A
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  2. #2
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    Hello, rsportsman09!

    I need to derive D from the following.

    . . \begin{array}{ccc} {\color{blue}(1)} & A \wedge B \\<br />
{\color{blue}(2)} & C \to D \\ {\color{blue}(3)} & C \:\vee \sim A \end{array}

    I'll give you the game plan ... You can supply the reasons.


    From (1), A and B are true . . . Hence: A is true. .(a)

    From (3), we have: .  C \:\vee \sim A \;\;=\;\;\sim A \vee C \;\;=\;\;A \to C .(b)


    We have: . \begin{array}{cccc}{\color{blue}(b)} & A \to C \\ {\color{blue}(2)} & C \to D \\  & --- \\ {\color{blue}(c)} & A \to D & \text{syllogism}\end{array}


    We have: . \begin{array}{cccc}{\color{blue}(c)} & A \to D \\ {\color{blue}(a)} & A \\ & --- \\ \therefore & D & \text{detachment}\end{array}

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