A certain illness has two symptoms associated with it - a fever and fatigue. There is a90% probability thatat leastone of the two symptomsoccurs for a randomly selected person with the illness. There is an 80% probability that a randomly selected person with the illness will come down with a fever and there is a 50% probability that a randomly selected person with the illness will feel fatigued.

Note: For simplicity, we will refer to the eventof "coming down with a fever" simply as "fever" and the event of "feeling fatigued" simply as "fatigue". You may do the same.

Please answer the following three questions:

1) Are the events of "fever" and "fatigue" complementary?

2) Are the events of "fever" and "fatigue" mutually exclusive (or disjoint)?

3) Are the events of "fever" and "fatigue" independent?

For each Question, provide your answer of Yes or No and appropriate numerical support andlogical reasoning for each answer.