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HW1 Solutions

# HW1 Solutions - CSE 20 Discrete Mathematics Spring 2010...

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Unformatted text preview: CSE 20: Discrete Mathematics Spring 2010 Problem Set 1 Solutions Instructor: Daniele Micciancio Due on: Thu. April 8, 2010 Problem 1 (6 points) Write down a parenthesized version of each of the following boolean formulas according to the standard precedence rules of boolean algebra: 1. ((( ¬ P ) ∨ Q ) → ( P ∧ R )) 2. P → (( Q ∨ ((( ¬ R ) ∧ S ) ∧ P )) → Q ) 3. ( A ∨ (( B ∧ C ) ∧ ( ¬ D ))) → A Problem 2 (10 points) For each of the following pairs of propositional formulas, determine if they are equivalent or not using the truth table method. Your solution should include (for each equivalence) the corresponding truth table and a brief sentence stating if the given equivalence is valid (or not) and why. 1. f = ( A → B ) ∧ ( A ∨ B ) ≡ B A B A → B A ∨ B f B 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2. f = ( A → B ) ∧ ( B → C ) → ( C → A ) 6 = A A B C A → B B → C ( A → B ) ∧ ( B → C ) C → A f A 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Problem 3 (10 points) Complete the following proof of the equivalence ( ¬ q → r ) → r ≡ q → r justifying each line with the name of the algebraic rule applied to it, and underlining the subformula the rule has been applied to. (As an example, the answer for the first step if provided.) You can use any rule from Theorem 2 from the textbookexample, the answer for the first step if provided....
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HW1 Solutions - CSE 20 Discrete Mathematics Spring 2010...

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