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Set theory

  1. Nov 8, 2008 #1

    ibc

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    1. The problem statement, all variables and given/known data
    just the very beginning of the course, a simple problem, but I don't know how to write it in the "formal" way, so I need help with that.


    2. Relevant equations
    Need to prove that
    A\(B\C) = (A\B)Ú(A∩C)
    (forget about the little line in the Ú, just the only thing I found =\ )


    3. The attempt at a solution
    I see why this is true, I just have no idea how to write it formally
     
  2. jcsd
  3. Nov 8, 2008 #2

    HallsofIvy

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    To prove X= Y you prove first "[itex]X\subset Y[/itex]" and then "[itex]Y \subset X[/itex]. To prove [itex]X\subset Y[/itex], you start "if x is in X and then use the what you know of X and Y to show that x must be in Y.
     
  4. Nov 8, 2008 #3

    ibc

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    ok, so I know if x is in A\(B\C), then x is in A and x is not equal to y, when y is all that is in B and not in C.
    so I know it's the same as saying "(A\B)Ú(A∩C)" but how do I say or write it, how do I "officially" prove that [itex]X\subset Y[/itex] in this case?
     
  5. Nov 8, 2008 #4

    HallsofIvy

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    No point is saying that x is NOT equal to something! That doesn't tell you what IS true of x.
    More to the point, x is in A and either x is NOT in B or x is in both B and C.
    If x is not in B then it is in which of (A\B) or (A∩C)?
    If x is B and in C the it is in which of (A\B) or (A∩C)?

    Does that show x is in "(A\B)Ú(A∩C)"?

    Now do it the other way.
     
  6. Nov 8, 2008 #5

    ibc

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    oo ok I see
    thanks
     
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