Simplify the following set expressions.

$(1)((AB)B)-(AB)$

$(2)((ABC)-(BC))A$

Let A and $B$ be sets, prove:

$(A-B)(B-A)=(AB)-(AB)$

Prove the following set identities.

$(1)A(BA)=BA$

Find the necessary and sufficient conditions for the following set equations to be satisfied.

$(1)(A-B)(A-C)=\frac{O}{?}$

$(2)(A-B)(A-C)=A$