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Difficult Predicate Logic Symbolization!

  1. Feb 15, 2012 #1
    1. The problem statement, all variables and given/known data

    I do not know if this is the right forum or subforum for this kind of topic. So if it is not, I apologize in advance.


    Symbolize the following sentence:

    Given that some mean elf will bite and some friendly one will too, the mean ones will bite whether or not provoked but the friendly ones will bite only if provoked.


    2. Relevant equations

    Fx: x is friendly
    Gx: x is mean
    Hx: x is an elf
    Ix: x will bite
    Jx: x is provoked


    3. The attempt at a solution


    This is my attempt and to me it seems right, but I could be missing one tiny simple thing.

    ∃x∃y(((Hx∧Gx∧Ix)∧(Fy∧Hy∧Iy))→((Jx∨∼Jx)→Ix)∧(Iy→Jy))
     
    Last edited: Feb 15, 2012
  2. jcsd
  3. Feb 15, 2012 #2

    lanedance

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    Homework Helper

    Ok, given I'm actually not that good at these...

    First for clarity and to simplify reading, I would probably use the folliwng nonmenclature (some good notation can simplify/clarify your problem immensly)
    E-Elf, M-Mean, F-Friendly, P-Provoked, B-Bites

    if I look at yours
    ∃x∃y(((Ex∧Mx∧Bx)∧(Fy∧Ey∧By))→((Px∨∼Px)→Bx)∧(By→Py) )

    first I note (Px∨∼Px) is always true, as the elf is either provoked or not, so I'm not sure you need that? so it becomes
    ∃x∃y(((Ex∧Mx∧Bx)∧(Fy∧Ey∧By))→(Bx)∧(By→Py)

    then I'd say both Bx and By are assumed true in the LHS, so are always true when the RHS is evaluated? so it becomes
    ∃x∃y(((Ex∧Mx∧Bx)∧(Fy∧Ey∧By))→Py

    Which doesn't tell us a heap... and then I would ask if you really need the x and the y to cover the two cases when the elf is mean or friendly, and whether friendly and mean were mutually exclusive so you could you assume friendly = (not mean), and the "for exists" only shows its true for some x and y, not all of them...

    So I was thinking you could simplify your approach by dropping the x and ys, and looking at it as follows...

    Given that some mean elf will bite and some friendly one will too,
    (is an elve and bites)
    the mean ones will bite whether or not provoked but the friendly ones will bite only if provoked.
    (implies either mean or friendly and provoked)
     
    Last edited: Feb 15, 2012
  4. Feb 15, 2012 #3
    Thanks for your time lanedance, but I am still stuck!
     
  5. Feb 15, 2012 #4

    lanedance

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    Homework Helper

    ok how about looking at the first bracketed comment, how would you write that?
     
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