{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mid2key-03_fixed

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

This preview shows pages 1–3. Sign up to view the full content.

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, finally, 9. with ¬ Ga to obtain the empty clause.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 negationslash = 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.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online