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Math Help - Logic, please check my answer

  1. #1
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    Logic, please check my answer

    Use a truth table to show that the argument given below (transitivity) is a valid argument form.

    p→q
    q→r
    -----
    ∴ p→r

    I am not 100% sure what I am supposed to be looking for, but I did construct the truth table. Does this look right?


    Logic, please check my answer-truth.bmp
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  2. #2
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    No, that is not correct.
    You need to add a column for \left( {p \to q} \right) \wedge \left( {q \to r} \right) .
    Again add a column for \left( {p \to q} \right) \wedge \left( {q \to r} \right)\to \left( {p \to r} \right) .
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  3. #3
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    Quote Originally Posted by Plato View Post
    No, that is not correct.
    You need to add a column for \left( {p \to q} \right) \wedge \left( {q \to r} \right) .
    Again add a column for \left( {p \to q} \right) \wedge \left( {q \to r} \right)\to \left( {p \to r} \right) .

    Why do I need to and them? And when it is all said and done, I want to see that I have a tautology?
    Attached Thumbnails Attached Thumbnails Logic, please check my answer-truth.bmp  
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