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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) Non-negative reals (c) Positive integers (d) Non-negative integers 14. Section 1.4, exercise 52 Please write how many hours (to the nearest quarter-hour) it took you to complete this as-signment near where you write your name on the ﬁrst page....
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- Winter '08
- Logic, Logical connective, First-order logic, Modus ponens, Discrete Structures Autumn