3.5 A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 7 days for this installation and check to take place. Let A be the event “it will be more than 4 days before the machinery becomes available”

and B be the event “it will be less than 6 days before the machinery becomes available.”

a. Describe the event that is the complement of event A.

b. Describe the event that is the intersection of events A and B.

c. Describe the event that is the union of events A and B.

d. Are events A and B mutually exclusive?

e. Are events A and B collectively exhaustive?

f. Show that 1A > B2 < 1A > B2 = B.

g. Show that A < 1A > B2 = A < B.