Problem_Set_01

Problem_Set_01 - ArsDigita University Month 2 Discrete...

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ArsDigita University Month 2: Discrete Mathematics - Professor Shai Simonson Problem Set 1 – Logic, Proofs, and Mathematical Reasoning 1. Logic Proofs. a. Prove that a b is equivalent to ¬ b ¬ a using a truth table. b. Prove it using algebraic identities. c. Prove that a b is not equivalent to b a . 2. Aristotle’s Proof that the Square Root of Two is Irrational. a. Prove the lemma, used by Aristotle in his proof, which says that if n 2 is even, so is n. (Hint: Remember that a b is equivalent to ¬ b ¬ a ). b. Prove that the square root of 3 is irrational using Aristotle’s techniques. Make sure to prove the appropriate lemma. c. If we use Aristotle’s technique to prove the untrue assertion that the square root of 4 is irrational, where exactly is the hole in the proof? d. Using the fact that the square root of two is irrational, prove that sin ( π /4) is irrational. 3. In ADU-ball, you can score 11 points for a goal, and 7 for a near miss. a. Write a Scheme program that prints out the number of goals and the number of near misses to achieve a given total greater than 60.
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This document was uploaded on 10/01/2011.

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Problem_Set_01 - ArsDigita University Month 2 Discrete...

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