Give short arguments for each part below to complete the reasoning. Please do not use Venn diagrams.
a. Prove that $A = (A\setminus B) \cup (A \cap B)$. (Hint: You should prove that $(A\setminus B)\cup (A\cap B) \subseteq A$ and vice-versa)
b. Prove that $(A \setminus B) \cap (A \cap B) = \emptyset$ (Hint: Try a proof by contradiction for this statement.).
I'm not too sure exactly where to start on this. Both statements make sense logically, but I don't know how exactly to prove them. Can anyone point me in the right direction?