Understanding set theory

  1. I'm trying to prove something small with set theory and since I'm new to it, I've run into a problem. I can't understand what the following means exactly and how to proceed further. Or where the mistake is, if there is one. I think there is, because it seems... freaky.

    [tex]x\notin\left(\left(\left(A\cup B\right)\setminus\left(A\cap B\right)\right)\cap C\right)[/tex]
    [tex]x\notin\left(\left(A\cup B\right)\setminus\left(A\cap B\right)\right)\wedge x\notin C[/tex]
    [tex]\left(x\notin\left(A\cup B\right)\wedge x\in\left(A\cap B\right)\right)\wedge x\notin C[/tex]
    [tex]\left(\left(\left(x\notin A\right)\vee\left(x\notin B\right)\right)\wedge\left(\left(x\in A\right)\wedge\left(x\in B\right)\right)\right)\wedge x\notin C[/tex]

    I'd post the entire thing of which this is a small part of, but that's my homework and I don't want to get into the habit of having other people do my homework for me. Plus I want to learn how and why it works, not just do it.
     
  2. jcsd
  3. matt grime

    matt grime 9,395
    Science Advisor
    Homework Helper

    consider this

    x is not an element of UnV
    x is not an element of U AND x is not an element of V

    you've said those two statements are equivalent (I think, since you've not actually said what your deductions are from line to line). find a counter example to show this is false.

    negation switches conjunction and disjunction, or union and intersection.

    similar observations hold for the other steps in your reasoning.
     
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