Midterm1_sol - Solutions to Midterm 1 Question 1 (a)...

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Solutions to Midterm 1 Question 1 (a) Someone has both been to every state and doesn’t know everyone. (b) It is not the case that every book that has been made into a movie is liked by everyone. (OR, there is a book that has been made into a movie and someone doesn’t like the book.) Question 2 (a) x ¬∀ yD ( x, y, Klondike bar ) or x y ¬ D ( x, y, Klondike bar ) . (b) Let B ( s ) = student s goes to beach, H ( s ) = student s finishes their home- work. xH ( x ) B ( x ) Question 3 ¬∃ x y ( P ( x ) ∧ ∃ z ( Q ( x ) → ¬ R ( y, z ))) ≡∀ x y ¬ ( P ( x ) ∧ ∃ z ( Q ( x ) → ¬ R ( y, z ))) ≡∀ x y ( ¬ P ( x ) ∨ ¬∃ z ( Q ( x ) → ¬ R ( y, z ))) ≡∀ x y ( ¬ P ( x ) ∨ ∀ z ¬ ( Q ( x ) → ¬ R ( y, z ))) ≡∀ x y ( ¬ P ( x ) ∨ ∀ z ¬ ( ¬ Q ( x ) ∨ ¬ R ( y, z ))) ≡∀ x y ( ¬ P ( x ) ∨ ∀ z ( Q ( x ) R ( y, z ))) Question 4 1
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( ¬ p q ) ( ¬ q r ) [( ¬ p q ) ∨ ¬ q ] [( ¬ p
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Midterm1_sol - Solutions to Midterm 1 Question 1 (a)...

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