Can someone help me with set proofs?

[Seth1288]

I've got something like this.
[MATH](A \setminus B) \cap (C \setminus D) = (A \cap C) \setminus (B \cup D)[/MATH]How can i transform this into logical statements?
I've got something like this but i don't know where to find laws.

[MATH](x \in A \land x \notin B) \cap (x \in C \land x \notin D) <=> (x \in A \land \neg x \in B) \land (x \in C \land \neg x \in D)[/MATH]can somebody explain next steps step by step with description? it would be great

 

[Steven G]

Why not (x∈(A∧C)∧(x∉(B∪D)) ??

 

[pka]

[MATH](A \setminus B) \cap (C \setminus D) = (A \cap C) \setminus (B \cup D)[/MATH]How can i transform this into logical statements?

\((A \setminus B) \cap (C \setminus D)\\(A\cap B^c)\cap(C\cap D^c)\\(A\cap C)\cap(B^c\cap D^c)\\(A\cap C)\cap(B\cup D)^c\\(A\cap C)\setminus(B\cup D)\)