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Math Help - [SOLVED] Logic proof which I am having trouble understanding

  1. #1
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    Question [SOLVED] Logic proof which I am having trouble understanding

    We have been given the following as an example of a proof, but I can not follow it.
    (b(1)=C OR b(1) ≠ C) AND (b(1)=C AND b(2)=J OR b(1)=J AND b(2)=C), (b(1)=C AND b(1) = J)=F
    --------------------------------------...
    (b(1)=C AND b(2)=J) OR (b(1) ≠ C) AND (b(1)=J AND b(2)=C)
    --------------------------------------...
    b(1) ≠ C OR b(2) = J
    -------------------------------------
    b(1) = C -> b(2) = J

    I see what happens from the second to last step but I'm unsure about the rest. Could someone please explain? Thanks
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  2. #2
    Senior Member Danneedshelp's Avatar
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    I think for the last step, the writter just used the fact that (\sim P) \vee Q  \Leftrightarrow P \Rightarrow Q.
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  3. #3
    Senior Member Danneedshelp's Avatar
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    Note: I am not sure why the first statement (B(1)=C \vee B(1) \neq C) stuck around, because P  \vee(\sim P) is a tautology.
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  4. #4
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    Quote Originally Posted by harihari View Post
    We have been given the following as an example of a proof, but I can not follow it.
    (b(1)=C OR b(1) ≠ C) AND (b(1)=C AND b(2)=J OR b(1)=J AND b(2)=C), (b(1)=C AND b(1) = J)=F
    --------------------------------------...
    (b(1)=C AND b(2)=J) OR (b(1) ≠ C) AND (b(1)=J AND b(2)=C)
    --------------------------------------...
    b(1) ≠ C OR b(2) = J
    -------------------------------------
    b(1) = C -> b(2) = J

    I see what happens from the second to last step but I'm unsure about the rest. Could someone please explain? Thanks

    CAN you write more clearly the proof you are given as an example in steps,because the way the proof is given makes no sense.

    WHAT IS given and what is the conclusion here??
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  5. #5
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    Thanks everyone, I worked it out
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  6. #6
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    This exactly how the proof was given by the way but it has been explained now
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