## Understanding set theory

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.

$$x\notin\left(\left(\left(A\cup B\right)\setminus\left(A\cap B\right)\right)\cap C\right)$$
$$x\notin\left(\left(A\cup B\right)\setminus\left(A\cap B\right)\right)\wedge x\notin C$$
$$\left(x\notin\left(A\cup B\right)\wedge x\in\left(A\cap B\right)\right)\wedge x\notin C$$
$$\left(\left(\left(x\notin A\right)\vee\left(x\notin B\right)\right)\wedge\left(\left(x\in A\right)\wedge\left(x\in B\right)\right)\right)\wedge x\notin C$$

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.

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 Recognitions: Homework Help Science Advisor 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.