This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ....
View
Full
Document
This note was uploaded on 03/21/2012 for the course CMPSC 40 taught by Professor Egiceoclu during the Spring '09 term at UCSB.
 Spring '09
 Egiceoclu

Click to edit the document details