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Math Help - Help with Proofs - Did I do this correctly?

  1. #1
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    Help with Proofs - Did I do this correctly?

    (Sorry if is in the wrong topic - I didn't see one for proofs)

    I am still trying to get the hang of my proofs class, and I was wondering if I did this problem correctly. The statements above the line are what is given, and below the line are my arguments & reasons that I came up with.

    Directions: Derive R

    (1) P ^ Q
    (2) (P v Q) -> R
    -----------------------------
    (3) P ..........(1) Simplification
    (4) Q ..........(1) Simplification
    (5) P v Q .....(3),(4) Addition
    (6) R ...........(2),(5) Definition of implication

    If I did something wrong, could you please explain what to do? Thanks in advance!
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  2. #2
    A Plied Mathematician
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    You didn't do anything wrong. I'd say you could eliminate line 4 altogether, though. You can introduce line 5 without line 4.
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  3. #3
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    Well we turned in the homework yesterday and went over it. Turns out that for the reason for step (6), I should have put Modus Ponens instead of Definition of Implication... Oh well. Now I know for next time.
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  4. #4
    A Plied Mathematician
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    Yeah, I'd agree it was Modus Ponens for the last step. I didn't know exactly what you meant by "definition of implication", so I let it pass. The idea was clearly valid.
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  5. #5
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    Yeah, I guess I had forgotten about Modus Ponens when I was doing that problem, so I thought to myself, "Well, if the first part of an implication is proven to be true, then the second part has to be true" and for some reason I just assumed that that was the case because that's how implications are... Oh well, I understand what I did wrong. Thanks again for your help
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  6. #6
    A Plied Mathematician
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    You're very welcome. Have a good one!
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