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3202f11-mid2 - • Sign the ±ERPA release on the next page...

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1. (10) Determine whether the following expressions are sets or families of sets. In these expressions, A and B are sets, F and B are families of sets, and { A i : i I } and { B i : i I } are indexed families of sets. You do not need to show your work. a. A ( intersectiontext F ). set family b. { A p : p I is prime } . set family c. ( uniontext F ) ( intersectiontext G ). set family d. P ( A ) ∩ { B i : i I } . set family e. P ( uniontext ( F ∪ G )). set family 1
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2. (30) Prove that for all integers n , n 2 + n is even. 2
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3. (30) Prove that for all sets A and B , if A Δ B A then B A . 3
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4. (30) Let F and G be families of sets. Prove that if uniontext F negationslash⊆ uniontext G then there is some A ∈ F such that for all B ∈ G , A negationslash⊆ B . 4
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NAME : MHF 3202 — Sets and Logic — Fall 2011 October 14, 2011 Midterm 2 Instructions: This is a closed book exam and no notes are allowed. You are not to provide or receive help from any outside source during the exam except that you may ask the instructor for clarification of a problem. You have 50 minutes and you should attempt all problems.
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Unformatted text preview: • Sign the ±ERPA release on the next page only if you wish your exam returned in lecture. • Calculators or other computing devices are not allowed. • Except where indicated, you must show all work and give a reason (or reasons) for your answer. A correct answer with incorrect work will be considered wrong. FERPA Release : Because of privacy concerns, I will not return your graded exams in lecture without your permission. If you want me to return your exam in lecture, please sign on the line indicated below. Otherwise, you may collect your exam during my oFce hours. SIGN HERE: . Problem Points Score 1 10 2 30 3 30 4 30 Total 100 Projected Grade — Note : The projected grade listed above is an estimate of the grade you would receive if the course ended right now....
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