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Unformatted text preview: • All good students study hard. • No students in mathematics are unable to use a computer. • ∀ x ∃ y x = y 2 9. Prove or disprove the claim that the compound proposition ∀ x P ( x ) ∨ ∀ x Q ( x ) is logically equivalent to ∀ x ( P ( x ) ∨ Q ( x )) 10. Section 1.3, exercise 62 11. Prove or disprove the claim that the proposition ∀ x ( P ( x ) → Q ( x )) is logically equivalent to ∀ x P ( x ) → ∀ x Q ( x ) (more on next page) 12. Section 1.4, exercise 8 13. Determine the truth value of ∃ x ∀ y ( x ≤ y 2 ) when the universe of discourse is the (a) Positive reals (b) Nonnegative reals (c) Positive integers (d) Nonnegative integers 14. Section 1.4, exercise 52 Please write how many hours (to the nearest quarterhour) it took you to complete this assignment near where you write your name on the ﬁrst page....
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 Winter '08
 Staff
 Logic, Logical connective, Firstorder logic, Modus ponens, Discrete Structures Autumn

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