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1. In a high school class of 100 students, 42 studied mathematics, 68 studied psychology, 54...

1. In a high school class of 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and psychology, 7 studied history but niether mathematics nor pychology, 10 studied all three subjects, and 8 took none of these. Randomly selecting a student from the class, what is the probability of the following event that: (a) a person enrolled in psychology takes all three subjects. (b) a person not taking psychology is taking both history and mathematics. 2. Suppose S = {1, 2, 3, 4, 5, 6}. Let E = {3, 5}, F = {1, 4, 5}, and G = {1, 2}. Compute the following sets and write

in set notation (as done for S, E, F, and G). Note that AB is regarded as A ∩ B. (a) EF G0 (b) E ∪ (F ∩ G) (c) (E ∪ F) ∩ (E ∪ G) (d) E(F ∪ G) (e) (EF) ∪ (EG) (f) (EF0 ) ∪ G (g) E(F 0 ∪ G)

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