Midterm1 Practice Problems FA09

# Midterm1 Practice Problems FA09 - MATH 347 MIDTERM 1...

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Unformatted text preview: MATH 347 MIDTERM 1: PRACTICE PROBLEMS The test will be given on Wednesday, October 7 . It will be based on Homeworks 1-5 (part of Chapters 1-3). In preparing for the test, you can practice solving the problems from the list below. In addition, take a look at the homework problems (at least one problems on the midterm will come directly from the homework), and at the examples given in the textbook. Update: Please ignore Problems 8 and 9, as they refer to the material not yet covered in class. 1. Problem 1.29 from the textbook. 2. Suppose P and Q are logical statements. Prove that the following sentences are tau- tologies: (a) ( P ⇒ Q ) ∨ ( Q ⇒ P ); (b) (( ¬ Q ∨ Q ) ⇒ P ) ⇔ P ; (c) ( ¬ Q ∧ Q ) ⇒ P . 3. Prove that, for any non-negative integer n , 3 divides 2 · 4 n + 1. 4. Prove that, for any positive integer n , 2 n summationdisplay k =1 ( − 1) k +1 k = 2 n summationdisplay j = n +1 1 j ....
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