How to prove $A = (A \cap B) \cup (A - B)$ and show that $(A \cap B)$ and $(A - B)$ are non-intersecting. I thought about starting with $A = (A \cap B) \cup (A)$ since $(A-B)$ is essentially saying only consider $A$. This would then lead me to proving $A = (A \cap B)$. However I'm completely stuck on how to prove they are non-intersecting.

HINT
You can use $A - B = A \cap B^C$ 
