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Predicate logic inference problem

  1. Jul 29, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the following question

    Adams is a boy who does not own a car. Mary dates only boys who own
    cars.Therefore Mary does not date Adams.


    2. Relevant equations



    3. The attempt at a solution
    My answer is like this...
    Let Bx=x is a boy.
    Ox=x owns car
    Dxy=x Dates y
    a=Adams
    m=Mary
    Accordingly we can translate sentences as


    1)Ba&~Oa
    2)for all x (Bx&Ox->Dmx)
    -----------------------
    2) can be written as Ba&Oa->Dma (by universal specification)
    further 2 can be reduced to
    3) Ba->(Oa->Dma) (By law of exportation)
    4) Oa->Dma (from p->q and p so q)
    5) ~Oa (From p&q so q)
    So, "we cant conclude that Mary does not date Adams".

    Am i wrong? If i'm please explian me where it went wrong. Thanks in advance.
     
  2. jcsd
  3. Aug 3, 2011 #2

    Mark44

    Staff: Mentor

    It seems to me that your conclusion is wrong. I am not up on predicate logic, so can't point out where you are going wrong. To belong to the set of boys whom Mary dates, a boy must own a car. Adams doesn't own a car, so he is not a member of that set. The conclusion is that Mary doesn't date Adams.
     
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