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Math Help - Ploys and Quoys

  1. #1
    Member Mr Rayon's Avatar
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    Ploys and Quoys

    The following questions are based on a set of propositions I-IV

    I All Ploys are Quoys
    II Some Ploys are not Quoys
    III Some, but not all, Ploys are Quoys
    IV No Ploys are Quoys

    Considered only by themselves, which of the following statements could both be true and false.

    A) I II
    B) II III
    C) I III
    D) I IV
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  2. #2
    MHF Contributor
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    I need to think of a good Ploy in order to answer this
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  3. #3
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    Hello, Mr Rayon!

    Some clarification, please.


    The following questions are based on a set of propositions I-IV

    I All Ploys are Quoys
    II Some Ploys are not Quoys
    III Some, but not all, Ploys are Quoys
    IV No Ploys are Quoys

    Considered only by themselves, which of the following statements could both be true and false.

    . . (A) I, II. . (B) II, III . . (C) I, III . . (D) I, IV

    Since no statement can be true and false,
    . . you evidently mean something else.

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  4. #4
    Member integral's Avatar
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    I All Ploys are Quoys
    II Some Ploys are not Quoys
    III Some, but not all, Ploys are Quoys
    IV No Ploys are Quoys

    I=\theta
    II=\gamma
    III=\delta
    IV=\alpha

    \gamma \longleftrightarrow \delta

    \theta \oplus \alpha
    (\gamma \longleftrightarrow \delta) \oplus (\theta \oplus \alpha)


    \textrm{So If}\,\,\, \theta\,\,\, \textrm{is false, then any other may be true}
    \textrm{ If}\,\,\,\gamma\,\,\, \textrm{is true, then} \,\,\,\delta \,\,\,\textrm{must be true. If these are both true then}\,\,\, \alpha\,\,\, \theta \,\,\, \textrm{are both false}

    \textrm{ If}\,\,\,\alpha \,\,\, \textrm{is true, then all others are false}

    So.

    Considered only by themselves, which of the following statements could both be true and false.

    A) \theta,\gamma
    B) \gamma,\delta
    C) \theta,\delta
    D) \theta,\alpha
    We know from
    (\gamma \longleftrightarrow \delta) \oplus (\theta \oplus \alpha) that theta & gamma can not be true, theta and delta can not both be true, and theta and alpha can not be true.

    But, If alpha is true theta and gamma can both be false (but not true see )
    Theta and delta can both be false if alpha is true( but not true).
    \theta and alpha can not both be false.

    But!
    If gamma is true, then delta is true. And if delta is false, then gamma is false.


    Te answer is delta and gamma.

    Edit: I had the attachment wrong for some time. Anyone who read this before and clicks on the attachment, please look at it once more.
    Attached Thumbnails Attached Thumbnails Ploys and Quoys-truth.png  
    Last edited by integral; March 28th 2010 at 08:36 PM.
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  5. #5
    Member Mr Rayon's Avatar
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    integral, you are correct!
    sorry, for any late reply, my internet's been very slow.
    How long did it take you to solve the problem? I'm doing an exam that tests your problem solving and logical reasoning skills. Got any advice on how one can improve this ability?
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  6. #6
    Member integral's Avatar
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    Took me about 10min to figure it out in my head, but the hard part is not solving it is showing how you got (which took about 20 more min) it if that makes sense.

    Also for the other question, I am not good at logic and reasoning, in fact I suck. It was not a hard question.

    Also, if you look at my reasoning, it has holes and incorrect information. I just could not think of how to word it any better.
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