# hw6 - CSE 260 Homework 6- Proofs ANSWER October 2, 2007 1....

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CSE 260 Homework 6- Proofs – ANSWER October 2, 2007 1. Section 1.5: 5, 29, 30 Section 1.6: 17, 39 Section 1.7: 3, 4 2. Consider problem 27 of section 1.5 on page 74 of the text book. (a) Give propositions for the two hypothesis and the conclusion by ap- plying appropriate universal and existential instantiations. Hypothesis 1: x ( P ( x ) ( Q ( x ) S ( x ))) universal instantiation: P ( a ) ( Q ( a ) S ( a )) ¬ P ( a ) ( Q ( a ) S ( a )) ( ¬ P ( a ) Q ( a )) ( ¬ P ( a ) S ( a )) Hypothesis 2: x ( P ( x ) R ( x )) universal instantiations: P ( a ) R ( a ) Conclusion: x ( R ( x ) S ( x ) universal instantiations: R ( a ) S ( a )) (b) Convert the above propositions into clauses. Hypothesis 1: Clauses: ¬ P ( a ) Q ( a ) and ¬ P ( a ) S ( a ) Hypothesis 2: clauses: P ( a ) and R ( a ) Conclusion: clauses: R ( a ) and S ( a ) (c) Prove the above conclusion based on refutation procedure ( i.e., derive a contradiction based on resolution inference rule.)

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## This note was uploaded on 04/28/2008 for the course CSE 260 taught by Professor Saktipramanik during the Fall '08 term at Michigan State University.

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hw6 - CSE 260 Homework 6- Proofs ANSWER October 2, 2007 1....

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