h1 - • ∀ x ∀ y P x y • ∀ x ∃ y P x y[10 Which...

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[40] Homework 1. Basic Logic Each problem is worth 10 points [10] Make truth tables for the following statements: 1. p ( r q ); 2. ( p ∧ ¬ q ) r . [10] Using logical equivalences discussed in class prove that ( p q ) ( p q ) is a tautology, that is, prove that ( p q ) ( p q ) T. [10] Let P ( x, y ) : x + y 5 where x, y positive integers . Tell whether the following statements are true or false:
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Unformatted text preview: • ∀ x ∀ y P ( x, y ) • ∀ x ∃ y P ( x, y ). [10] Which of the following is equivalent to ∀ x ∃ y P ( x, y ) ≡ ¬∀ x ∃ y P ( x, y ): (a) ∃ x ∀ y P ( x, y ); (b) ∀ x ∃ y P ( x, y ); (c) ∃ x ∀ y P ( x, y ); (d) ∃ x ∃ y P ( x, y ). 1...
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