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exercise3sol - CSE541 EXERCISE 3 SOLUTIONS Reminder We...

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Unformatted text preview: CSE541 EXERCISE 3 SOLUTIONS Reminder: We define H semantics operations ∪ and ∩ as follows a ∪ b = max { a,b } , a ∩ b = min { a,b } . The Truth Tables for Implication and Negation are: H-Implication ⇒ F ⊥ T F T T T ⊥ F T T T F ⊥ T H Negation ¬ F ⊥ T T F F QUESTION 1 We know that v : V AR-→ { F, ⊥ ,T } is such that v * (( a ∩ b ) ⇒ ( a ⇒ c )) = ⊥ under H semantics. evaluate v * ((( b ⇒ a ) ⇒ ( a ⇒ ¬ c )) ∪ ( a ⇒ b )). Solution : v * (( a ∩ b ) ⇒ ( a ⇒ c )) = ⊥ under H semantics if and only if (we use shorthand notation) ( a ∩ b ) = T and ( a ⇒ c ) = ⊥ if and only if a = T,b = T and ( T ⇒ c ) = ⊥ if and only i f c = ⊥ . I.e. we have that v * (( a ∩ b ) ⇒ ( a ⇒ c )) = ⊥ iff a = T, b = T,c = ⊥ . Now we can we evaluate v * ((( b ⇒ a ) ⇒ ( a ⇒ ¬ c )) ∪ ( a ⇒ b )) as follows (in shorthand notation). v * ((( b ⇒ a ) ⇒ ( a ⇒ ¬ c )) ∪ ( a ⇒ b )) = ((( T ⇒ T ) ⇒ ( T ⇒ ¬ ⊥ )) ∪ ( T ⇒ T )) = ((...
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exercise3sol - CSE541 EXERCISE 3 SOLUTIONS Reminder We...

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