Proving statement $(A \cup C)\setminus B=(A\setminus B)\cup C \iff B\cap C= \varnothing$ I want to prove the following statment:
$$(A \cup C)\setminus B=(A\setminus B)\cup C \iff B\cap C= \varnothing$$
Do I need to prove each side? Or is one side enough? I mean, if I get from the left side to the right is it enough?
How do the following statements help me?


*

*$(A \cup C) \setminus B = (A \cup C)\cap B'$

*$(A \setminus B) \cup C = (A \cap B')\cup C$


I would like to get some hint to prove this statement.
Thanks!

You can use an approach like in my answer to your other similar question.  Let me know if you like a fuller answer, and I'll update.
