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A logical question

  1. Sep 29, 2008 #1
    ilai,bob,gon,dany are students from a large number of student

    which are divided into two classes.

    the director has 4 requests regarding the placement of these 4 students.

    A.gon and dany want to be in the same class
    B.ilai and dany dont want to be in the same class
    C.bob and ilai want to be in the same class
    D.dany and bob want to be in the same class

    the director checked the combined requests and found a logical in the combined
    product.she decided to ignore one request
    but still she got a logical error when combined the left ones.

    which one of the requests are being ignored by the director?

    i think its request 2 which is being ignored:
    from arguments A and c we get this division:

    first class:

    second class:

    but arguments D says that dany and bob want to be in the same class
    which is not possible

    why the answer of the book is 1
  2. jcsd
  3. Sep 30, 2008 #2
    B, C, and D are circular. That means that no matter what you do, you cannot arrange the students such that B, C, and D are all satisfied. You can easily determine this by noticing that Gon only appears in A, whereas the other students each appear in 2 or more conditions. The options are:

    1. (Bob, Dany, Gon, Ilai) () - Violates B
    2. (Bob, Dany, Gon) (Ilai) - Violates C
    3. (Bob, Dany, Ilai) (Gon) - Violates A,B
    4. (Bob, Gon, Ilai) (Dany) - Violates A,D
    5. (Dany, Gon, Ilai) (Bob) - Violates B,C,D
    6. (Bob, Dany) (Gon, Ilai) - Violates A,C
    7. (Bob, Gon) (Dany, Ilai) - Violates A,B,C,D
    8. (Bob, Ilai) (Dany, Gon) - Violates D

    If you ignore B, then you can go with arrangement 1, and all the remaining conditions are satisfied. If you ignore C, then you can go with arrangement 2 with no problems. If you ignore D, then you can choose arrangement 8 with no errors.

    But if you ignore A, you still cannot arrange the students in any way that will satisfy B, C, and D.

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