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Final Exam Solution

# Final Exam Solution - Name Math 243 Spring 2006 Professor...

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Name: Math 243, Spring 2006, Professor Callahan Final Exam, Tue., May 9 Note 1: This test is closed book. You may use one 8 1 2 × 11 sheet of notes (both sides). Note 2: Show your work. Clarity counts. If I can’t follow your reasoning I can’t give credit. Problem 1: Of a classroom of 25 students, 12 are men and 13 are women. 15 are engineering majors and 10 are sophomores. 6 are male engineering majors, 6 are sophomore engineering majors and 5 are sophomore men. 2 are male sophomore engineering majors. How many women are there in the class who are neither sophomores nor engineering majors? Answer: Let M be the set of men in the class, E be the set of engineering majors and S be the set of sophomores. By the inclusion–exclusion principle, | M E S | = | M | + | E | + | S |- | M E |- | M S |- | E S | + | M E S | = 12 + 15 + 10 - 6 - 6 - 5 + 2 = 22 . Thus 22 of the 25 students are men or sophomores or engineering majors. The number of people who are none of these things is therefore 3.

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