Unformatted text preview: ) Exercise 19. Negate the following statements in a meaningful way. a. The product of two rational numbers is rational. b. The product of two irrational numbers is irrational. Exercise 20. Determine if each of the statements in the previous problem is true or false, and justify your answer. (Hint: Recall that a statement is false if its negation is true.) Exercise 21. a. Explain why the statements ∀ x ( P ( x ) ∧ Q ( x )) and ( ∀ x ( P ( x ))) ∧ ( ∀ x ( Q ( x ))) should be considered logically equivalent. b. Find an example that shows ∃ x ( P ( x ) ∧ Q ( x )) and ( ∃ x ( P ( x ))) ∧ ( ∃ x ( Q ( x ))) are not logically equivalent....
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 Fall '09
 Math, Logic, Irrational number, meaningful way

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