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5615H_MT1

# 5615H_MT1 - Math 5615H Name(Print October 5 2011 Midterm...

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Math 5615H. October 5, 2011. Midterm Exam. Name (Print) 60 points are distributed between 5 problems. You have 50 minutes (2:30 pm – 3:20 pm) to work on these problems. No books, no notes. Calculators are permitted, however, for full credit, you need to show step-by-step calculations. This booklet consists of 7 page: the title page (this one), 5 pages (pp. 2–6) contain 5 problems. The almost empty page 7 can also be used for solutions. Some definitions: The union of sets { E α , α A } [ α A E α := { x : α A such that x E α } . The intersection of sets { E α , α A } \ α A E α := { x : α A, x E α } . The complement of E X E c := { x X : x / E } . These operations satisfy the following properties: 1. Distributivity: A ( B C ) = ( A B ) ( A C ) . 2. DeMorgan’s Laws: ( i ) [ α A E α · c = \ α A E c α , ( ii ) \ α A E α · c = [ α A E c α .

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Math 5615H. October 5, 2011. Midterm Exam. Page 2. Problem 1. (10 points). Let A and B be nonempty bounded subsets of R . Show that sup( A B ) = sup { sup A, sup B } .
Math 5615H. October 5, 2011. Midterm Exam.

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