hw05 (1)

# hw05 (1) - Spring-2011 CMSC 250 Homework 5 Due Wed Mar 2...

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Unformatted text preview: Spring-2011 CMSC 250: Homework 5 Due: Wed Mar 2, 2011 NOTE: Due AT THE BEGINNING of Recitation! COURSE WEBSITE: http://www.cs.umd.edu/ ∼ gasarch/250/S11.html (NOTE- there is a Tilda before gasarch. It may be easier to get to the course website via the dept webpage (go to class webpages) or gasarch’s homepage (it will be obvious).) 1. (0 points) What is your name? Write it clearly. Staple your HW. 2. (25 points) Simplify the following formula ¬ ( ∃ x )( ∀ y )[ ¬ R ( x,y ) ∧ ( Q ( x,y ) ∨ ¬ S ( x,y ))] . SOLUTION TO PROBLEM 2 We use the rules for negation and quantifiers to obtain ¬ ( ∃ x )( ∀ y ) ≡ ( ∀ x )( ∃ y ) ¬ . Hence we get ( ∀ x )( ∃ y )[ ¬ [ ¬ R ( x,y ) ∧ ( Q ( x,y ) ∨ ¬ S ( x,y ))]] . We use De Morgan’s law and ¬¬ X ≡ X to obtain ( ∀ x )( ∃ y )[ R ( x,y ) ∨ ( ¬ Q ( x,y ) ∧ S ( x,y ))]] . 3. (30 points) In this problem the only domains we allow in the answers are subsets of R ....
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hw05 (1) - Spring-2011 CMSC 250 Homework 5 Due Wed Mar 2...

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