7eTestBankUpdated

7eTestBankUpdated - 464 Test Bank Questions and Answers...

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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 13? 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 48, 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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This note was uploaded on 03/21/2012 for the course CMPSC 40 taught by Professor Egiceoclu during the Spring '09 term at UCSB.

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7eTestBankUpdated - 464 Test Bank Questions and Answers...

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