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Math Help - Requesting aid with some formalization questions

  1. #1
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    Requesting aid with some formalization questions

    Really stuck with this. Any help appreciated.

    Domain of dicourse: company employees


    Sx: x is a secretary
    Bx: x is a bookeeper
    Exy: x is paid more than y
    Dx: x should be dismissed
    Wxy: x is wary of y

    C: the CEO


    1 Every secretary earns more than a bookkeeper
    2 No secretary earns more than the CEO
    3 Any secretary who earns more than every bookkeeper should be dismissed
    4 Every bookkeeper who is a secretary earns more than a
    bookkeeper who is not
    5 Some bookkeepers are wary of every secretary
    6 Everyone is wary of someone, but only secretaries who are not bookkeepers are wary of everyone
    7 There is a secretary who is a bookkeeper and is wary of all secretaries who are not bookkeepers
    8 Not all bookkeepers are secretaries but all secretaries are bookkeepers
    9 If any secretary earns more than every bookkeeper, Adams does.

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  2. #2
    MHF Contributor
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    Re: Requesting aid with some formalization questions

    Welcome to the forum.

    I assume you need to write these statements in symbolic form. What difficulties are you having? Here are the first two statements; you try the rest.

    1. \forall x\forall y\,S(x)\land B(y)\to E(x,y) (I assume the original statement means "...more than every bookkeeper").

    2. \neg\exists x\,S(x)\land E(x,\mathrm{CEO}) (I assume CEO is a constant and not a predicate symbol).
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  3. #3
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    Re: Requesting aid with some formalization questions

    Thanks for your help - I have managed to get through it ok
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