1. You complete an experiment by rolling a six sided fair die. The following events are defined:
(1) A = {1,3,4}; (2) B = {2,4,6}; (3) C = {3}; (4) D = {3,5,6}; (5) E = {1,3,5};
(6) F = {5,6}.
Determine the following events.
(a) $A \cup D$.
(b) $A \cap D$.
(c) $B \cap E$.
(d) $A^c$.
(e) $B^c \cap C$.
(f) $(B \cup C)^c$.
(g) State whether the following statements are true of false. If false, state why it is false.
(i) A and C are mutually exclusive.
(ii) A and F are mutually exclusive.
(iii) $F \subset A^c$.
(iv) $F \subset E$.
