Independent

Independent Event
Definition) Two events A, and B are independent if and only if
$P(A\cap B)=P(A)\cdot P(B)$
$P(A|B)= \frac{ P(A \cap B)}{P(B)}=P(a)$, where P(B) > 0
 
Example 1.) Mathematical Statistics by K.Knight. Chapter 1, 1.2
Suppose that A and B are independent events. Determine which of the following pairs of events are always independent and which are always disjoint.
(a) A and $B^c$
(c) $A^c$ and $B^c$  
Solution??!!