3.89 State, with evidence, whether each of the following statements is true or false:

a. The complement of the union of two events is the intersection of their complements.

b. The sum of the probabilities of collectively exhaustive events must equal 1.

c. The number of combinations of x objects chosen from n is equal to the number of combinations of 1n - x2 objects chosen from n, where 1 … x … 1n - 12.

d. If A and B are two events, the probability of A, given B, is the same as the probability of B, given A, if the probability of A is the same as the probability of B.

e. If an event and its complement are equally likely to occur, the probability of that event must be 0.5.

f. If A and B are independent, then A and B must be independent.

g. If A and B are mutually exclusive, then A and B must be mutually exclusive.