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Math Help - Checking Predicate Logic

  1. #1
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    Checking Predicate Logic

    I am not confident I have done this exercise properly.
    I have to get it in by Monday 12th PM. Any advice much appreciated,

    UD: Persons
    Ex: x is a real estate agent
    Rx: x is rich
    Lx: x is a lawyer
    Yx: x is a yuppie
    Axy: x respects y

    1. all real estate agents are yuppies x (Ex --> Yx)
    2. no real estate agents are yuppies x (Ex --> ~Yx)
    3. some but not all real estate agents are yuppies x (Ex ∧ ~Yx)
    4. some real estate agents are yuppies and some are not x (Ex ∧ Yx)
    5. if any real estate agent is a yuppie then all are x (Ex ---> Yx)
    6. any real estate agent who is not a yuppie is not rich x (Ex ∧ ~Yx) --> Rx
    7. yuppies who are not rich don’t exist x (Yx --> Rx)
    8. every yuppie respects some lawyer x [Yx --> ( y)(Ly∧ Axy)]
    9. no lawyer respects himself x~ (Yxx)
    10. every self-respecting real estate agent is rich x (Exx ---> Rx)
    11. some lawyer respects every real estate agent (y)(Lx∧(y) (Ey --> Axy))
    12. anyone who is a real estate agent and a lawyer is a yuppie and rich
    x [(Ex∧Lx) -->(Yx∧Rx)]
    13. no real estate agent respects every lawyer x (Ex --> (y) (Lxy)
    14. real estate agents and lawyers are rich if they are yuppies x ((Ex ∨ Lx) ∧ Yx) --> Rx
    15. real estate agents and lawyers are rich only if they are yuppies
    x ((Ex ∨ Lx) ∧ Rx) --> Yx


    Thank you for any help checking this
    Last edited by mr fantastic; December 12th 2011 at 03:13 AM. Reason: Title.
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  2. #2
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    Re: Looking for urgent help checking Predicate Logic

    There is no definition for the Bx predicate. Moreover, 10 and 13 use Bxx and Bxy.

    Check 3-6, 9, 11.
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  3. #3
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    Re: Looking for urgent help checking Predicate Logic

    Sorry about that - I have corrected the post.
    Hope you have time to re-check.
    3 & 4 seem like the same answer but it cant be true?

    Appreciate any help. Thank you
    Last edited by garrypark; December 11th 2011 at 01:50 PM.
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  4. #4
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    Re: Looking for urgent help checking Predicate Logic

    Quote Originally Posted by garrypark View Post
    Sorry about that - I have corrected the post.
    Hope you have time to re-check.
    3 & 4 seem like the same answer but it cant be true?
    Why do you say that?
    But is a conjunctive.
    To say "Not all estate agents are yuppies" means \left( {\exists x} \right)\left[ {E(x) \wedge \neg Y(x)} \right].
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  5. #5
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    Re: Looking for urgent help checking Predicate Logic

    I have put the answer you have given me above as my answer to some estate agents are yuppies and some are not!! So how is this different to not all estate agents are yuppies?? Please excuse me but this is my first attempt at predicate logic.
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  6. #6
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    Re: Looking for urgent help checking Predicate Logic

    To do 3 and 4, write two formulas: (1) some real estate agents are yuppies, (2) some real estate agents are not yuppies. Then take a conjunction of these formulas.
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  7. #7
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    Re: Looking for urgent help checking Predicate Logic

    Great -just in the nick of time
    thanks
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