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.(adsbygoogle = window.adsbygoogle || []).push({});

[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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Understanding set theory

**Physics Forums | Science Articles, Homework Help, Discussion**