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Math Help - Natural Deduction in propositional logic

  1. #1
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    Natural Deduction in propositional logic

    I am trying to solve this but I am not too sure whether I am doing this right

    p V ( q ʌ r)
    ----------
    p V q


    and I know this can be proved using V-E rule.

    But I just don't know the step maybe because i am new to this thing. Please help me..
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  2. #2
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    Re: Natural Deduction in propositional logic

    There are several flavors of natural deduction: Fitch style, tree style with formulas as nodes and tree style with sequents as nodes. The following is a derivation in tree style with formulas (the picture is clickable).

    Natural Deduction in propositional logic-deriv2.png

    Fee free to ask further questions if this format is not clear.
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  3. #3
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    Re: Natural Deduction in propositional logic

    if you don't mind could you please represent this in Fitch style so that I can check whether I 've got this right? thank you very much Mr. emakarov!
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  4. #4
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    Re: Natural Deduction in propositional logic

    Fitch style is something like this.

    Code:
    1. p \/ (q /\ r)	Assumption
    2.   p			Assumption
    3.   p \/ q		2, \/I
    4.   q /\ r		Assumption
    5.   q			4, /\E
    6.   p \/ q		5, \/I
    7. p \/ q		1,2-3,4-6, \/E
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  5. #5
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    Re: Natural Deduction in propositional logic

    Thank you for your kindness
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