> 
> Let A and B be two random events associated with a random experience.
>  Show that:
> 
> 
> $A \cap B = B \setminus (\bar{A} \cap B)$
> 
> 
> 

As stated in the course, given a random event $A$, the definition of $\bar{A}$ is $\Omega \setminus A$. So I thought I could do something like this:
$A \cap B = B \setminus ((\Omega \setminus A) \cap B)$. $(\Omega \setminus B) $ is going to be $B$ since $\Omega$ includes $B$. So the expression becomes: $B \setminus B$ which is $\emptyset$. This is, obviously, a wrong result. 

How is this proof done?