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Unformatted text preview: ( B ⇒ ¬ A )) ≡ negimpl (( A ∩ ¬¬ B ) ∩ ( B ∩ ¬¬ A )) ≡ dneg (( A ∩ B ) ∩ ( B ∩ A )) ≡ assoc,comm ( A ∩ B ). QUESTION 3 We deﬁne an EQUIVALENCE of LANGUAGES as follows: Given two languages: L 1 = L CON 1 and L 2 = L CON 2 , for CON 1 6 = CON 2 . We say that they are logically equivalent , i.e. L 1 ≡ L 2 1 if and only if the following conditions C1, C2 hold. C1: For every formula A of L 1 , there is a formula B of L 2 , such that A ≡ B, C2: For every formula C of L 2 , there is a formula D of L 1 , such that C ≡ D. Prove that L {¬ , ∩ , ⇒} ≡ L {↑} . HINT: use ¬ a = a ↑ a , a ∪ b = ( a ↑ a ) ↑ ( b ↑ b ). 2...
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This note was uploaded on 02/12/2011 for the course CSE 541 taught by Professor Bachmair,l during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Bachmair,L
 Computer Science

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