99Se2 - 1 1a. Prove Theorem 2.7g, namely: Let A and B be...

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MARK BOX problem points 1 10 2 10 3 10 4 10 5 10 Total 40 % 100 Math 300X.001 Prof. Girardi Spring 99 Exam 2 4/6/99 NAME: INSTRUCTIONS : 1. Do 4 of the 5 problems. I am doing problem numbers: . 2. Use your own paper: a. write on only one side of the page b. begin each (numbered) problem on a new page c. put your name on each page d. put your pages in order. 3. For problems that request a proof, write a neat formal proof. 4. During this test, do not leave your seat. If you have a question, raise your hand. 5. This closed book/notes exam covers, from A Transition to Advanced Mathematics ,4 th Ch 2 . Problem Source : 1. from class lecture 2. from class lecture 3. hand-in problem 2.3 # 6b 4. Ch 2: Extra Practice Problems # 16 5. hand-in problem 2.5 # 2.
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Unformatted text preview: 1 1a. Prove Theorem 2.7g, namely: Let A and B be sets. Show that ( A B ) C = A C B C . 1b. Theorem 2.7g is commonly referred to as s Law. 2. Prove part of Theorem 2.5, namely: Let A and B be sets with A B . Show that P ( A ) P ( B ). hint : You may use, without proving, Theorem 2.2. 3. Let I = { A : } be an indexed family of sets and let B be a set. Show that B [ \ A ! = \ B [ A . 4. Use the PMI to show that 1 2 + 2 2 + . . . + n 2 = n ( n + 1)(2 n + 1) 6 for each natural number n . 5. Let a 1 = 2 a 2 = 4 a n +2 = 5 a n +1-6 a n for all n > 1 . Show that a n = 2 n for all natural numbers n . 2...
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99Se2 - 1 1a. Prove Theorem 2.7g, namely: Let A and B be...

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