HW2 - CSE 20: Discrete Mathematics Spring 2010 Problem Set...

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Unformatted text preview: CSE 20: Discrete Mathematics Spring 2010 Problem Set 2 Instructor: Daniele Micciancio Due on: Thu. April 15, 2010 Problem 1 (6 points) Formulate each of the following statements in English (without using mathematical symbols) and assert which one is true or false: 1. ∀ x ∈ Z . ∃ y ∈ Z .x < y 2. ∃ y ∈ Z . ∀ x ∈ Z .x < y Problem 2 (10 points) Complete the proof of the following theorem by filling the gaps. Theorem 1. If p → ¬ q and q ∨ r , then p → r . Proof. Given and , we need to prove . In order to prove p → r , we assume is true, and show that follows. We give a proof by cases. Since is given, either or is true. We consider the following two cases: • Case 1 ( is true): In this case r is true and there is nothing to be proved. • Case 2 ( is true): Since p → is given and is true by assumption, we can deduce . But we also have . This proves q ∧¬ q which is a contradiction. So, also in this case r follows....
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This note was uploaded on 09/24/2011 for the course CSE 20 taught by Professor Foster during the Fall '08 term at UCSD.

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HW2 - CSE 20: Discrete Mathematics Spring 2010 Problem Set...

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