How to prove $( \cap )\setminus ( \cap ) = \cap (−)$? I need to prove this statements using the laws....
I tried this
\begin{align*}
&( \cap ) \setminus ( \cap )\\  
& ( \cap ) \cap ( \cap )'\\  
& ( \cap ) \cap (' \cup ')
\end{align*}
Then I got stuck...
I tried the right side as well...but end up getting this
\begin{align*}
&  \cap ( \setminus )\\   
& A \cap ( \cap ')
\end{align*}
And got stuck again.
So I want the steps for both sides.  Thanks.

one very elementary way to prove such things is to show
$$
x\in (A\cap B)\setminus (A\cap C) \quad\Rightarrow\quad x\in A\cap (B\setminus C)
$$
and the converse
$$
x\in A\cap (B\setminus C)\quad\Rightarrow\quad (A\cap B)\setminus (A\cap C)
.
$$

Your attempt can be continued by the rule $A\cap (B \cup C) = (A\cap B) \cup (A\cap C)$. So applying this to your last step yields
\begin{align}
(A\cap B) \cap (A^\complement \cup C^\complement) &= \underbrace{\big((A\cap B)\cap A^\complement\big)}_{=\emptyset} \cup \big((A\cap B) \cap C^\complement\big)
=A \cap (B \cap C^\complement)
=A \cap (B \setminus C) 
\end{align}
