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practice_exam_1

# practice_exam_1 - PRACTICE EXAM 1 Some notation A B A is...

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PRACTICE EXAM 1 Some notation: A B : A is logically equivalent to B Γ | = A : Γ logically implies A A * : The “dual” of A 1. True or False (2pts each) (1) If A A 0 , then A ∨ ¬ A 0 is a tautology. (2) If A B is a contradiction, then A is not a contradiction. (3) If ( A → ¬ A ) A is contradiction, then A is not a contradiction. (4) If A is a contradiction, then ¬ A B is a tautology. (5) If A B ∨ ¬ B and A C B ∨ ¬ B , then A C . (6) If A B , then the dual of ¬ A B is a tautology. (7) If Γ is inconsistent and Γ 0 Γ, then Γ 0 is inconsistent. (8) If A is a contradiction, then A } is consistent. (9) If { A 1 , ..., A n } is inconsistent, then A 1 , ..., ¬ A n } is consistent. (10) If Γ is inconsistent and Γ Γ 0 , then Γ 0 is inconsistent. (11) If A B , then A * B * . (12) A ( A * ) * (13) If A ( B ( C D )) is not a tautology, then A is a contradiction. (14) If A ≡ ¬ B * , then A * ≡ ¬ B . (15) If { A 1 , ..., A n } is consistent, then { A * 1 , ..., A * n } is consistent.

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