Let $A,B$ and $C$ are three events then which of the following statement$($s$)$ is$/$are

correct?

A$.$ If $P(AB)0$ then $P(ABC)=P(A)P(\frac{B}{A})P(\frac{C}{AB}).$

B$.$ If A and $B$ are independent then $A^C$ and $B$ need not be independent.

C$.P(\frac{C}{B})+P(\frac{C}{B^C})=1$

D$.$ If $A,B$ and $C$ are independent then $AB$ and $C$ may be dependent.