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Math Help - [SOLVED] Knights and Knaves help >__<

  1. #1
    TGS
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    [SOLVED] Knights and Knaves help >__<

    Two natives A and B address you as follows:

    A says: Both of us are knights.
    B says: A is a knave.

    What are A and B?

    Okay, so I assume that A is telling the truth so:

    (a ^ b)

    and since B is a knight then what B says has to be true so:

    ~a

    Then there's the contradiction:

    a ^ ~a

    The negation law states:

    c

    ...and that's how far I got.. -____-

    I don't even know if I'm doing this correctly.
    Last edited by TGS; September 29th 2009 at 07:51 PM.
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  2. #2
    MHF Contributor
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    Hello TGS
    Quote Originally Posted by TGS View Post
    Two natives A and B address you as follows:

    A says: Both of us are knights.
    B says: A is a knave.

    What are A and B?

    Okay, so I assume that A is telling the truth so:

    (a ^ b)

    and since B is a knight then what B says has to be true so:

    ~a

    Then there's the contradiction:

    a ^ ~a

    The negation law states:

    c

    ...and that's how far I got.. -____-

    I don't even know if I'm doing this correctly.
    I assume that a knight always tells the truth and a knave always lies.

    So let a be the proposition "A is a knight", and b be the proposition "B is a knight"

    Then a \Rightarrow (a\land b), since A says "Both of us are knights"

    Therefore a\Rightarrow b

    Therefore a\Rightarrow B tells the truth

    Therefore a\Rightarrow \neg a, since B says "A is a knave".

    Contradiction.

    Therefore a is false, and A is therefore a knave.

    Now \neg b \Rightarrow B always lies

    Therefore \neg b \Rightarrow a, since B says "A is a knave"

    Contradiction.

    Therefore \neg b is false. Therefore B is a knight.

    Grandad

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