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Unformatted text preview: CS 165A – Artiﬁcial Intelligence, Winter 2011, Assignment #3 – Propositional Logic
Due before class on February 8, 2011 Notes
• Be sure to re-read the “Policy on Academic Integrity” on the course syllabus. • Any updates or corrections will be posted on the Announcements page (home page for the course), so check there occasionally. • Hand in your copy in the class (please use a word processing editor). • Important: Keep your answers precise and concise. Avoid writing a monograph! A few sentences are plenty for each part of your answer. Exercises
7.6 Prove, or ﬁnd a counterexample to, each of the following assertions: a. If α |= γ or β |= γ (or both) then (α ∧ β ) |= γ b. If α |= (β ∧ γ ) then α |= β and α |= γ . c. If α |= (β ∨ γ ) then α |= β or α |= γ (or both). 7.10 Decide wheater each of the following sentences is valid, unsatisﬁable, or neither. Verify your decisions using truth tables or the equivalence rules of Figure 7.11 (page 249). c. (Smoke ⇒ F ire) ⇒ (¬Smoke ⇒ ¬F ire) f. (Smoke ⇒ F ire) ⇒ ((Smoke ∧ Heat) ⇒ F ire) g. Big ∨ Dumb ∨ (Big ⇒ Dumb) 1 2 ...
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This note was uploaded on 02/22/2011 for the course CS 165A taught by Professor Su during the Spring '11 term at UCSB.
- Spring '11
- Artificial Intelligence