4. Using the fact (A U B) = A° N B°, prove De Morgan's second law (ANB) = Aº U Bº. 5. During a year, the probability a structure will be damaged by an earthquake (A) is 0.02, that it will be damaged by a hurricane (B) is 0.03, and that it will be damaged by both is 0.007. What is the probability that it will not be damaged by a hurricane or an earthquake during that year? 6. Consider the following statement: Let A, B, C be three events. If P(A) + P(B) + P(C) = 1, then the events A, B, C are mutually exclusive. Is this statement true or false? If true, prove it and if false find a counterexample. 1. An electrical unit consists of four components each of which is subject to failure. Suppose that, at a specified time, we observe this unit to determine which components are working and which have failed. Write the sample space associated with this random experiment. 2. Suppose the sample space is S = {x|-8≤ x ≤8}. Let A = {x|−2 < x < 2}, B = {x| − 3 < x < -1}, and C = {x|1 < x < 3}. Determine the set (A NBN c)' 3. Two dice are rolled. E is the event sum on the two dice is odd and F is the event there is at least one 1 on the dice. Assume the dice are distinct. List the elements of the events (a) EnF (b) Ec n Fc