Different Ass3-Solutions & answers.pdf

Different Ass3-Solutions & answers.pdf - Assignment 3...

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Assignment 3 Solutions CSE2309/3309 CSC2091/3091 - Artificial Intelligence CSE2309/3309 CSC2091/3091 Artificial Intelligence - Assignment 3 (Propositional Logic and First Order Predicate Calculus) Solutions from Richard Nichols and Lam Phuong Lam Question 1 F : The French team will win at least one gold medal. G : The German team will win at least one gold medal. D : The Danish team will win at least one gold medal. P : The French team is plagued with injuries. S : The star German runner is disqualified. R : It rains during most of the competition. a. At least one (of the three teams) will win a gold medal. b. At most one of them will win a gold medal. ( F ¬ G ¬ D ) ( ¬ F G ¬ D ) ( ¬ F ¬ G D ) ( ¬ F ¬ G ¬ D ) or ( F ¬ G ¬ D ) ( ¬ F G ¬ D ) ( ¬ F ¬ G D ) ( ¬ F ¬ G ¬ D ) c. Exactly one of them will win a gold medal. ( F ¬ G ¬ D ) ( ¬ F G ¬ D ) ( ¬ F ¬ G D ) d. Provided it doesn't rain during most of the competition and their star runner isn't disqualified, the Germans will win a gold medal if either of the other teams does. ( ¬ R ¬ S ( F D ) ) G e. The Germans will win a gold medal only if it doesn't rain during most of the competition and their star runner is not disqualified. Page 1 D G F ) ) (( ) ( G S R D F ¬ ¬ D G )) ( ( )) ( ( )) ( ( F G D D F G D G F ¬ ¬ ¬ ¬ ¬ ¬ ]) [ ( ]) [ ( ]) [ ( G D F F G D F D G ¬ ¬ ¬ ¬ ¬ ¬
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Assignment 3 Solutions CSE2309/3309 CSC2091/3091 - Artificial Intelligence ( ¬ R ¬ S ) G (AN: Note "only if" is opposite direction to "if") Page 2 ) ( S R G ¬ ¬
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Assignment 3 Solutions CSE2309/3309 CSC2091/3091 - Artificial Intelligence Question 2 a. (Smoke Fire) ( ¬ Smoke ¬ Fire) Convert to clausal form: : (Smoke Fire) ( ¬ Smoke ¬ Fire) = ¬ ( ¬ Smoke Fire) (Smoke ¬ Fire) = (Smoke ¬ Fire) Smoke ¬ Fire Now construct truth table: Smoke Fire ¬ Fire Smoke ¬ Fire (Smoke ¬ Fire) Smoke ¬ Fire T T F F T T F T T T F T F F F F F T F T From the result column it can be seen that this expression is neither valid nor unsatisfiable . b. Smoke Fire ¬ Fire Already in clausal form: Smoke Fire ¬ Fire Now construct truth table: Smoke Fire ¬ Fire Smoke Fire ¬ Fire T T F T T F T T F T F T F F T T From the result column it can be seen that this expression is always true, therefore -- valid . Page 3
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Assignment 3 Solutions CSE2309/3309 CSC2091/3091 - Artificial Intelligence c. [(Smoke Heat) Fire] [(Smoke Fire) (Heat Fire)] Convert to clausal form: : [(Smoke Heat) Fire] [(Smoke Fire) (Heat Fire)] = [ ¬ (Smoke Heat) Fire] [( ¬ Smoke Fire) ( ¬ Heat Fire)] = ( ¬ Smoke ¬ Heat Fire) ( ¬ Smoke Fire ¬ Heat Fire) = ( ¬ Smoke ¬ Heat Fire) ( ¬ Smoke Fire ¬ Heat) = ¬ Smoke ¬ Heat Fire Now construct truth table: Heat Smoke Fire ¬ Smoke ¬ Heat ¬ Smoke ¬ Heat Fire T T T F F T T T F F F F T F T T F T T F F T F T F T T F T T F T F F T T F F T T T T F F
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  • Fall '08
  • First-order logic, clausal form, Quad Erat Demonstrandum

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