03Fe2 - 2. a variation on an extra practice problem and on...

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Prof. Girardi Math 300.001 Fall 2003 11.11.03 Exam 2 MARK BOX problem points 1 10 2 10 3 10 4 10 total 30 NAME: SSN: INSTRUCTIONS : (1) Do 3 of the 4 problems. I am doing problem numbers: . (2) Use your own paper or the scratch paper I provided: write on only one side of the page begin each (numbered) problem on a new page put your name on each page (3) For problems that request a proof, write a neat formal proof and use only logic and the definitions of the concepts involved (i.e., do not quote a problem from the book). You may include your skeleton, if you so wish, but points will be given for your formal proof only. (4) The mark box indicates the problems along with their points. Check that your copy of the exam has all of the problems. (5) During this exam, do not leave your seat. If you have a question, raise your hand. When you finish: turn your exam over, put your pencil down, and raise your hand. (6) This closed book/notes exam covers (from A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre: 5 th ed.): Chapter 2 . Problem Inspiration : 1. an example from class and also from my 99 Spring exam 2
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Unformatted text preview: 2. a variation on an extra practice problem and on a look-at problem 3. from another textbook 4. from another textbook Numbers: real numbers = R natural numbers = N = { 1 , 2 , 3 , 4 , . . . } integers = Z = { , 1 , 2 , 3 , 4 , . . . } rational numbers = Q = n p q R : p, q Z and q 6 = 0 o 1 1. Let A and B be sets. 1a. By denition, the power set of A is: P ( A ) = { C : } . 1b. Let A B . Show that P ( A ) P ( B ) . 2. Let A = { A i : i N } be an indexed family of sets. Let k, m N with k m . Show that m \ i =1 A i k \ i =1 A i . 3. Let a 1 = 1 and a 2 = 3 and a n +2 = 3 a n +1-2 a n for each n N . 3a. Calculate a 1 through a 5 . 3b. Show that a n =-1 + 2 n ( * ) for each n N . 4. Let a 1 = 1, a 2 = 1, and a 3 = 1 and a n +3 = a n +2 + a n +1 + a n for each n N . 4a. Calculate a 1 through a 6 . 4b. Show that a n 2 n-2 ( * ) for each n N with n > 1 . 2...
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This note was uploaded on 12/13/2011 for the course MATH 300 taught by Professor Staff during the Fall '11 term at South Carolina.

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03Fe2 - 2. a variation on an extra practice problem and on...

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