State, with evidence, whether each of the following statements is true or false:
a. The probability of the union of two events cannot be less than the probability of their intersection.
b. The probability of the union of two events cannot be more than the sum of their individual probabilities.
c. The probability of the intersection of two events cannot be greater than either of their individual probabilities.
d. An event and its complement are mutually exclusive.
e. The individual probabilities of a pair of events cannot sum to more than 1.
f. If two events are mutually exclusive, they must also be collectively exhaustive.
g. If two events are collectively exhaustive, they must also be mutually exclusive.