hw2 - CSE 20: Discrete Mathematics Fall 2011 Problem Set 2...

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CSE 20: Discrete Mathematics Fall 2011 Problem Set 2 Instructor: Daniele Micciancio Due on: Wed. October 12, 2011 This homework assignment is based on Sections 1.2 and 1.3 of the textbook. Problem 1 (12 points) In class we proved (using the truth table method) that the following derivation rule (called “proof by cases”) is valid: if p q , p r and q r are all true, then r is also true. (In symbols, ( p q ) , ( p r ) , ( q r ) = r .) In this problem, you will give a formal proof sequence that “proof by cases” is a valid derivation rule. Complete the following proof sequence for the inference ( p q ) , ( p r ) , ( q r ) = r by providing a justification for each line. The justification should include the name of the derivation rule used, and the line numbers of the statements it is applied to. As justification you can use any of the equivalence rules in Table 1.3 or inference rules in Table 1.4 at page 18-19 of the textbook, as well as “given” and the “distributive property” p ( q r ) ( p q ) ( p r ) from Exercise 1.1, 14(b) on page 11. (As an example of proof sequences with justifications, see Examples 1.7, 1.8 and 1.9 in the textbook.)
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This note was uploaded on 11/21/2011 for the course CSE 20 taught by Professor Foster during the Spring '08 term at UCSD.

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hw2 - CSE 20: Discrete Mathematics Fall 2011 Problem Set 2...

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