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A logical question

  1. Aug 15, 2008 #1
    a monkey , giraffe , elephant and a tiger are living in 4 cages as its described in the
    drawing in this link:
    http://img397.imageshack.us/my.php?image=16670586ic0.gif

    which one of this arguments doesn't settle with with the other three arguments?

    1.the giraffe is living between the floor of the elephant and the floor of the monkey
    2.the tiger is not living above the elephant.
    3.in a floor which is located between the floor where lives the elephant and the floor
    where lives the giraffe ,lives only one animal.
    4. in a floor which is located between the floor where lives the monkey and the floor
    where lives the tiger ,lives only one animal.

    i don't know from where to start
    so i started from top to bottom
    from 1 i can understand that the monkey and the elephant are separated .
    one of them lives in the first floor and the other lives in the third floor
    the giraffe lives in the second floor

    from 2 i can understand that in order for the tiger not to be above the elephant
    and without crossing the 1st argument ,we need to put the elephant in the 3rd floor
    and the tiger into one of the cages in the first floor.
    and the remaining places in the first floor goes to the monkey

    but in this way
    it crashes with both arguments 3 and 4

    what is the algorithm for solving such a question?
     
    Last edited: Aug 15, 2008
  2. jcsd
  3. Aug 15, 2008 #2

    DaveC426913

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    Argument 1,2 and 4 are true, argument 3 is false, in this arrangement:

    monkey
    giraffe
    tiger elephant
     
  4. Aug 15, 2008 #3
    where did i go wrong in the way that i presented

    what is the algorithm for solving such a question?
     
  5. Aug 15, 2008 #4

    Redbelly98

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    In this, and many other similar problems being posted, I am seeing a lot of strictly verbal answers / solutions.

    However, I pretty much always use charts and/or diagrams to solve these problems. To me, reasoning this out verbally is an incredibly inefficient way to go after the solution. Yes, you'll get there eventually, but with the stated goal of solving the problems in 2 minutes or less I can't imagine that using words alone will get you through the upcoming test.
     
  6. Aug 15, 2008 #5

    Redbelly98

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    The 1st and 3rd statements can be represented by the attached diagrams. Already we see that they are incompatible because of the giraffe's location. Make similar diagrams for statements 2 and 4, and try to make them consistent with either #1 or #3.
     

    Attached Files:

  7. Aug 15, 2008 #6

    DaveC426913

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    True if you can see the attached diagrams. If you can't you're SOOL...
     
  8. Aug 15, 2008 #7
    ok i understand that i need to use charts
    i did solved it using a chart
    i just expressed it verbally

    in cage 1 there is a there tiger
    in cage 2 there is a monkey
    in cage 3 there is a giraffe
    in cage 4 there is a elephant

    i do know what steps to do in order to solve this kind of question
    from which argument do i start?
    if this argument gives me a multiple possibilities for one member
    how do i write it down?
    or do i need to keep it in my head?

    how do i decide what argument to take next??

    i showed in the i tried to solve it
    that i got to a dead end because
    the way arranged the objects crossed with arguments 3 and 4

    i just don't know on what algorithm should i follow
    in order to solve it
     
  9. Aug 15, 2008 #8

    Redbelly98

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    Are you able to view my attached charts in post #5? I show how to write multiple possibilities ... you just draw a figure for each possibility, understanding that any one of them could be true.

    As for where to start, it shouldn't matter. Draw the diagrams that go with each statement, 1 through 4. I just showed #1 and #3 to provide an example, but you must do it for each statement.

    Also, are you aware that no arrangement of animals is consistent with all 4 statements? You are supposed to get a contradiction, and figure out which statement must be removed to get 3 consistent statements.
     
  10. Aug 15, 2008 #9

    Redbelly98

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    Yeah, there is that little glitch here. I forget because I'm able to view attachments.
     
  11. Aug 15, 2008 #10
    i your drawing
    when described the possibilities of argument 1
    there are more possibilities when the monkey is on the other cage in the same floor
    i completed the all the possibilities for all the arguments
    in this link:
    http://img181.imageshack.us/my.php?image=physicsforumslogicproblhp7.gif

    although as i said
    there could be more in argument 1 and argument 4
    what do i do know with all those possibilities?

    what is the next step?
     
  12. Aug 15, 2008 #11

    Redbelly98

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    I did leave out some possibilities concerning the lower floor; an animal on the lower floor could be in either the left or right hand cage. There are 2 ways to handle this:

    1. Include all the lower-floor possibilities every time we are showing an animal on the lower floor.
    or
    2. Notice that none of the statements distinguishes the 2 lower-floor cages. For example we don't have anything statement like "Animal A is to the left of Animal B, on the same floor". Since the 2 lower cages are equivalent, just keep in mind that an animal depicted in one lower-floor cage could just as easily occupy the other lower-floor cage.

    Option #1 is more straightforward. Option #2 saves some space because there are fewer figures to draw. It's really up to you which method you choose.

    First, you need to redo statement 2: the tiger is not above the elephant. So the tiger is either on the same level or below the elephant.

    After than, you just have to look over the figures. One statement is incompatible with the other 3. So look for some incompatibility among the figures somewhere.
     
  13. Aug 16, 2008 #12
    Last edited: Aug 16, 2008
  14. Aug 16, 2008 #13

    Redbelly98

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    I don't understand that statement. Sorry.

    Since the blue arrows you drew in your figure indicate a consistent arrangement of animals using statements 1, 2, and 4, it appears that you have solved it.

    If you want to be rigorous, you would need to see why the arrangements in #3 are all inconsistent with the ones indicated by blue arrows. However, on a standardized test like this it's not necessary to be rigorous.

    edit added:
    p.s. there is still a slight problem with some of your figures in #2, but luckily this does not affect the solution. You are drawing the tiger above the elephant in 2 figures, but the statement says the tiger is not above the elephant.
     
  15. Aug 16, 2008 #14
    i corrected my error in argument 2

    i managed to arrange all the objects
    ones using argument 1 and argument 4

    and the other way is with 1 and 2
    as i show in the link:
    http://img519.imageshack.us/my.php?image=physicsforumslogicproblhk2.gif

    i got the same arrangement from
    when i combined 1 and 2
    and when i combined 1 and 4

    i couldn't make an arrangement with three arguments

    ????
     
  16. Aug 16, 2008 #15

    Redbelly98

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    You came up with the following arrangement:

    M
    G
    E,T

    It is consistent with the following of your figures:
    #1, right-hand figure
    #2, upper-left figure
    #4, left-hand figure

    p.s. this doesn't affect the solution, but missing from figure set #2 is:

    E
    T
    _ , _
     
  17. Aug 16, 2008 #16
    ok thanks
    ill try to implement this in the next questions
     
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