mid2key-03_fixed

mid2key-03_fixed - CSci 5511 Spring 2003 Key for 2nd...

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CSci 5511 Spring 2003 Key for 2nd Midterm Exam 1. 15 points Use resolution to prove that ( S R ) is entailed by the following set of propositional expressions: 1. ¬ ( ¬ Q ) Z 2. ¬ W 3. ( ¬ W Q ) ( ¬ P ) 4. ( W Z ) S 5. Q ( S P ) 6. ( P Q ) R Answer: we convert to CNF and add the negated goal 1a. Q 1b. Z 2. ¬ W 3. W ∨ ¬ Q ∨ ¬ P 4. ¬ W ∨ ¬ Z S 5. ¬ Q S P 6. ¬ P ∨ ¬ Q R ¬ Ga . ¬ S ¬ Gb . ¬ R We resolve ¬ Gb . with 6. and obtain 7. ¬ P ∨ ¬ Q then 7. with 5. 8. ¬ Q S and 8. with 1a. 9. S and, ±nally, 9. with ¬ Ga to obtain the empty clause.
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2. 20 points (a) Write the following sentences in predicate calculus: 1. Every student has taken at least one computer science course. xStudent ( x ) ⇒ ∃ y CScourse ( y ) Take ( x,y ) 2. A student has taken at most one computer science course. xStudent ( x ) [ y CScourse ( y ) Take ( x,y ) [ zCScourse ( z ) z n = y ⇒ ¬ Take ( x,z )]] or, equivalently, xStudent ( x ) [ y CScourse ( y ) Take ( x,y ) [ zCScourse ( z ) Take ( x,z ) z = y ]] 3. Every student has been in every building on campus.
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This note was uploaded on 10/21/2011 for the course CSCI 5511 taught by Professor Staff during the Spring '08 term at Minnesota.

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mid2key-03_fixed - CSci 5511 Spring 2003 Key for 2nd...

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