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Math Help - [SOLVED] logic proof

  1. #1
    DarrenD
    Guest

    [SOLVED] logic proof

    by using the rules of inference how can I prove that:

    (AvB)n(AvC) concludes Av(BnC)

    I know how to prove it the other way round using rules of inference but when i try to prove it this way I get stuck. Here is my work:

    1 (AvB)n(AvC) hypothesis
    2 (AvB) n-elimination on line 1

    3 A Assumption
    4 Av(BnC) v-introduction on line 3

    5 B Assumption

    I don't know how to continue this proof using rules of inference. Any help appreciated.
    thanks.
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  2. #2
    Junior Member
    Joined
    Nov 2005
    Posts
    31

    truth table

    you cannot use a truth table?

    I assume the n is representing the 'and' sign, right?
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  3. #3
    Global Moderator

    Joined
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    Try using de Morgan's law.
    \neg (p\vee q)\leftrightarrow \neg p\wedge \neg q
    Thus,
    \neg [(A \vee B)\wedge (A \vee C)]
    becomes,
    \neg (A \vee B) \vee \neg (A \vee C)
    That is the form of using the law of inference.
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