Counting the Number of Elements in an Intersection A professor in a discrete mathematics class passes out a form asking students to check all the mathematics and computer science courses they have recently taken. The finding is that out of a total of 50 students in the class, 30 took precalculus; 18 took calculus; 16 took both precalculus and Java; 8 took both calculus and Java; 47 took at least one of the three courses. 26 took Java; 9 took both precalculus and calculus; (a) How many students took all the three courses? (b) How many students took precalculus and calculus but not Java? 2/8

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