Events A and B are independent events. Answer the following questions as true or false, then justify each of your answers. [This means that if the events in part (a)-(c) are independent, then show it. Else, provide the counter example] (a) A and B^c are independent. (b) A^c and B are independent. (c) A^c and B^c are not independent. (Use results from (a) to find answers for (b) and (c))