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Math Help - Help with Logic (Natural Deduction)

  1. #1
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    Help with Logic (Natural Deduction)

    Can anyone solve this using Natural Deduction rules? (ND)
    I have attached a file showing the same problem with better symbols.

    I ^ ~(TvD) -> R given
    D^N -> V given
    I -> ~T given



    N^~V -> R goal


    Thank you !!!
    Attached Files Attached Files
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  2. #2
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    I ^ ~(TvD) -> R given
    D^N -> V given
    I -> ~T given

    N^~V -> R goal
    I don't think it follows. I assume the parentheses are as follows:

    (I /\ ~(T \/ D)) -> R given
    (D /\ N) -> V given
    I -> ~T given

    (N /\ ~V) -> R goal

    Then what happens when I, V, R, D are false and T, N are true?

    If you can wait, I could look into this tomorrow morning. I like natural deduction!
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  3. #3
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    From what I see the problem is correct. (if I is false then R follows from the first given formula)
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  4. #4
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    If the parentheses are as I indicated and if I is false, the first formula is automatically true and does not say anything about R. I am not sure if I should try other ways to parenthesize or if there is something wrong with the problem statement...
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  5. #5
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    Hell, true; I don't know why when I saw the first formula true I deduced R was true... And I made that mistake twice before posting
    I don't know, I would have put the parentheses exactly as you did. Unless in the first formula, we have to read

    I\wedge (\neg(T\vee D)\rightarrow R) (but I find that strange)

    the problem statement may be wrong.
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  6. #6
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    <br />
(I\wedge \neg(T\vee D)) \rightarrow R\:\:\: given
     (D\wedge N) \rightarrow V \qquad\;\quad\: given
    I \rightarrow \neg T \qquad\qquad\qquad given



    (N\wedge \neg V ) \rightarrow R \qquad\quad goal<br />

    So thats more like!! The problem statements are correct I ve just put also the parentheses to make it easier to read.
    (Anyone can eliminate the parentheses using the parenthesis elimination rules!!) ! So any ideas...??
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  7. #7
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    Is there a difference with the version I gave above?
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  8. #8
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    No I just made it more readable....
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