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Unformatted text preview: 464 Test Bank Questions and Answers TEST BANK Questions for Chapter 1 What is the negation of the propositions in 1–3? 1. Abby has more than 300 friends on facebook. 2. A messaging package for a cell phone costs less than $20 per month. 3. 4 . 5 + 2 . 5 = 6 In questions 4–8, determine whether the proposition is TRUE or FALSE. 4. 1 + 1 = 3 if and only if 2 + 2 = 3. 5. If it is raining, then it is raining. 6. If 1 < 0, then 3 = 4. 7. If 2 + 1 = 3, then 2 = 3 1. 8. If 1 + 1 = 2 or 1 + 1 = 3, then 2 + 2 = 3 and 2 + 2 = 4. 9. Write the truth table for the proposition ¬ ( r → ¬ q ) ∨ ( p ∧ ¬ r ). 10. (a) Find a proposition with the truth table at the right. p q ? T T F T F F F T T F F F (b) Find a proposition using only p,q, ¬ , and the connective ∨ that has this truth table. 11. Find a proposition with three variables p , q , and r that is true when p and r are true and q is false, and false otherwise. 12. Find a proposition with three variables p , q , and r that is true when at most one of the three variables is true, and false otherwise. 13. Find a proposition with three variables p , q , and r that is never true. 14. Find a proposition using only p,q, ¬ , and the connective ∨ with the truth table at the right. p q ? T T F T F T F T T F F F 15. Determine whether p → ( q → r ) and p → ( q ∧ r ) are equivalent. 16. Determine whether p → ( q → r ) is equivalent to ( p → q ) → r . 17. Determine whether ( p → q ) ∧ ( ¬ p → q ) ≡ q . Test Bank Questions and Answers 465 18. Write a proposition equivalent to p ∨ ¬ q that uses only p,q, ¬ , and the connective ∧ . 19. Write a proposition equivalent to ¬ p ∧ ¬ q using only p,q, ¬ , and the connective ∨ . 20. Prove that the proposition “if it is not hot, then it is hot” is equivalent to “it is hot”. 21. Write a proposition equivalent to p → q using only p,q, ¬ , and the connective ∨ . 22. Write a proposition equivalent to p → q using only p,q, ¬ , and the connective ∧ . 23. Prove that p → q and its converse are not logically equivalent. 24. Prove that ¬ p → ¬ q and its inverse are not logically equivalent. 25. Determine whether the following two propositions are logically equivalent: p ∨ ( q ∧ r ) , ( p ∧ q ) ∨ ( p ∧ r ). 26. Determine whether the following two propositions are logically equivalent: p → ( ¬ q ∧ r ) , ¬ p ∨ ¬ ( r → q ). 27. Prove that ( q ∧ ( p → ¬ q )) → ¬ p is a tautology using propositional equivalence and the laws of logic. 28. Determine whether this proposition is a tautology: (( p → q ) ∧ ¬ p ) → ¬ q . 29. Determine whether this proposition is a tautology: (( p → ¬ q ) ∧ q ) → ¬ p ....
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 Spring '09
 Egiceoclu
 test bank questions

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