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(Real Analysis) Find sets E\F and f(E)\f(F)

  1. Aug 28, 2010 #1
    1. The problem statement, all variables and given/known data

    The problem #11.

    3. The attempt at a solution

    My partial answer is attached. There, I found E\F. I still don't understand what is f(E) and f(F) and how to derive them from E and F.

    Attached Files:

  2. jcsd
  3. Aug 29, 2010 #2
    From #10 we know that f(E) = f(F). Thus, f(E)\f(F) = {} = [tex] \emptyset. [/tex] Can you get the rest?
  4. Aug 29, 2010 #3


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    f(E) = {f(x) | x ∈ E}

    Does that make sense?
  5. Aug 29, 2010 #4

    So f(E\F) is (-1=<x<0), which is NOT a subset of an empty set.
  6. Aug 29, 2010 #5
    Not quite...almost there.

    E\F = { -1 =< x < 0 }, not f(E\F). Find f(E\F). The final step's still the same and obvious.
  7. Aug 29, 2010 #6
    My inability to understand is killing me. I am using this forum non-stop for the last 12 hours for Real Analysis questions. No progress on my part what so ever.
  8. Aug 29, 2010 #7
    How are you going about teaching this to yourself? Which textbook are you using? Any other resources?
  9. Aug 29, 2010 #8
    I only have one textbook, which is Real Analysis by Bartle and Sherbert. I've read the chapter many times and continue reading it. Thanks to your, Raskolnikov, comments, I have made some progress, but still very weak.
    I also have another online book. I haven't found any helpful online sources for dummies on Real Analysis.
  10. Aug 29, 2010 #9


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    E is a subset of the domain of the function f. f(E) is a subset of the codomain of f. It's the set that f maps elements of E onto.

    If y is an element of f(E), then there's some x in E such that f(x)=y.
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