3.4 Exercises: 1,3, 5, 11, 13, 19, 21, 41, 45, 47, 49 3.5 Exercises: 1, 3, 5, 13, 15

3.6 Exercises: 1, 3, 5, 11, 13, 17, 21, 25

Identify each statement as true or false. 45. 6 - 0 - 3 if and only if 0 + 2 - 10. 46. 3 + 1 # 7 if and only if & # 8. 47. 8 +7 x 15 if and only if 3 x 5 # 8. Exercises 57 and 58 refer to the Chapter Opener on 48. 6 x 2 - 18 if and only if 9 + 7 16. page 83. Humphrey the hero deduced from the rid- 49. George H. W. Bush was president if and only if George die that there are twin trolls W. Bush was not president. who take shifts guarding the magical doors. One of 50. McDonald's sells Whoppers if and only if Apple manu- them tells only trades, the factures Ipods. other only lies. When the troll standing guard sees Humphrey, he says, Two statements that can both be true about the same object are consistent. For example, "It is green" and "It weighs "If truly Truthful Troll I be, then go 60 pounds" are consistent statements. Statements that thon cast and be mhow free." cannot both be true about the same object are called contrary. "It is a Nissan" and "It is a Mazda" are contrary. Humphrey needs to decide which troll he is addressing. In Exercises 51-35, label each pair of statements as either call him by name, and tell him which door he would like contrary or consistent. opened. There are two things Humphrey must get right: the 51. Michael Jackson is alive. Michael Jackson is dead. name of the troll and the proper door. If he misidentifies the troll, no door will be opened. If he correctly names 52. That book is nonfiction. That same book costs more the troll and picks the wrong door, he will be confined to than $150. the dungeon behind it. 53. This number is a whole number. This same number is 57. Because the troll either always lies or always tells the truth, Humphrey knows that irrational. (1) if the troll is Truthful Troll, then the conditional 54. This number is positive. This came number is a natural statement he uttered is true, and number. (2) if the conditional statement he uttered is true, then he is Truthful Troll. 55. This number is an integer. This same number is a rational Let p represent "the troll is Truthful Troll" and let q rep- number. resent "the door to the cast leads to freedom." Express the statements in (1) and (2) in symbolic form. 56. Refer to the "For Further Thought" on page 99 at the end of Section 3.2. Verify that the logic circuit at the top of the next column (consisting of only NOR gates) 56. The conjunction of the answers from Exercise 57 is a biconditional that must be true. Is equivalent to the biconditional A + B. Build a truth table for the statement - (p x q) (the negation of the (a) Build a truth table for this biconditional. Exclusive OR statement). What is the relationship (b) Use the fact that it must be true to solve Hum- between this and the biconditional? phrey's riddle.Decide whether each argument is valid or invalid. 1. All amusement parks have thrill rides. 2. All disc jockeys play music. Universal Orlando is an amusement park. Calvin is a disc jockey. Universal Orlando has thrill rides. Calvin plays music. Scanned with CamScanner 122 CHAPTER 3 Introduction to Logic 3. All celebrities have problems. As mentioned in the text, an argument can have a true con That man has problems. clusion yet be invalid. In these exercises, each argument ha a true conclusion. Identify each argument as valid or invali That man is a celebrity. 17. All birds fly. 18. All actors have cars. 4. All Southerners speak with an accent. All planes fly. All cars use gas. Nick speaks with an accent. A bird is not a plane. All actors have gas. Nick is a Southerner. 19. All chickens have beaks. Bigol tonipho off: 5. All dogs love to bury bones. All hens are chickens. mass of momups Puddles does not love to bury bones. All hens have beaks. Puddles is not a dog 20. All chickens have beaks. Show .Spisumaa 6. All vice presidents use cell phones. Bob does not use a cell phone. 10 and All birds have beaks. gotwoy edvald Bob is not a vice president. All chickens are birds. 7. All residents of Colorado know how to breathe thin air. 21. Amarillo is northeast of El Paso. ga nicdoM Julie knows how to breathe thin air. Amarillo is northeast of Deming. monosg Julie lives in Colorado. El Paso is northeast of Deming. jab omne OM ,enwo 8. All drivers must have a photo I.D. 22. Beaverton is north of Salem. Kay has a photo I.D. Salem is north of Lebanon. momA DEton Kay is a driver. Beaverton is north of Lebanon. el ofal evomni6. All vice presidents use cell phones. 20. All chicke Bob does not use a cell phone. All birds have beaks. Bob is not a vice president. All chickens are birds. gotwoy edyald 7. All residents of Colorado know how to breathe thin air. 21. Amarillo is northeast of El Paso. ga nicdoM Julie knows how to breathe thin air. Amarillo is northeast of Deming. monose Julie lives in Colorado. El Paso is northeast of Deming. ab omne OM ,anwo 8. All drivers must have a photo I.D. 22. Beaverton is north of Salem. Kay has a photo I.D. Salem is north of Lebanon. Kay is a driver. Beaverton is north of Lebanon. 9. Some dinosaurs were plant eaters. 23. No whole numbers are negative. Danny was a plant eater. -3 is negative. Danny was a dinosaur. -3 is not a whole number. Iw ob of paidten 10. Some philosophers are absent minded. a valids sell 24. A scalene triangle has a longest side. Nicole is a philosopher. A scalene triangle has a largest angle. Nicole is absent minded. The largest angle in a scalene triangle is opposite the 11. Many nurses belong to unions. longest side. Heather is a nurse. Heather belongs to a union. In Exercises 25-30, the premises marked A, B, and Care followed by several possible conclusions. Take each con- 12. Some trucks have sound systems. clusion in turn, and check whether the resulting argument Some trucks have gun racks. is valid or invalid. Some trucks with sound systems have gun racks. A. All people who drive contribute to air pollution. 13. Refer to Example 3. If the second premise and the con- B. All people who contribute to air pollution make life clusion were interchanged, would the argument then a little worse. be valid? C. Some people who live in a suburb make life a little worse. 14. Refer to Example 4. Give a different conclusion from ieni the one given there so that the argument is still valid. 25. Some people who live in a suburb contribute to air pollution. Construct a valid argument based on the Euler diagram shown. 26. Some people who live in a suburb drive. 15. People with 16. blond hair Procedures RNs 27. Suburban residents never drive. can perform People with Procedures 28. Some people who contribute to air pollution live in a blue eyes LVNs can suburb. perform 29. Some people who make life a little worse live in a suburb.3.6 EXERCISES Each argument either is valid by one of the forms of valid 11. She uses e-commerce or she pays by credit card. arguments discussed in this section, or is a fallacy by one She does not pay by credit card. of the forms of invalid arguments discussed. (See the sum- She uses e-commerce. mary boxes.) Decide whether the argument is valid or a fal- lacy, and give the form that applies. 12. Mia kicks or Drew passes. 1. If Rascal Flatts comes to town, then I will go to the Drew does not pass. concert. Mia kicks. If I go to the concert, then I'll call in sick for work. Use a truth table to determine whether the argument is valid If Rascal Flatts comes to town, then I'll call in sick for or invalid work. 13. p V q 14. p A ~q 2. If you use binoculars, then you get a glimpse of the bald eagle -q If you get a glimpse of the bald eagle, then you'll be amazed. If you use binoculars, then you'll be amazed. 15. ~p =~q 16. p V ~q 3. If Marina works hard enough, she will get a promotion. p - q Marina works hard enough. 17. p- q 18. ~p-q She will get a promotion. q -p 4. If Isaiah's ankle heals on time, he'll play this season. PAq His ankle heals on time. 19. p-~q 20. p- -q He'll play this season. -P 5. If he doesn't have to get up at 3:00 A.M., he's ecstatic. toplo Brit nonT He's ecstatic. 21. (p - q) A (q-P) 22. (p / q) V (pvq) He doesn't have to get up at 3:00 A.M. P p V q p 6. "A mathematician is a device for turning coffee into theorems." (quote from Paul Erdos) 23. (~p V q) A (-p-q) 24. (rAP) - (rvq) You turn coffee into theorems. q AP r VP You are a mathematician. 25. (-P Ar) - (pvq) 26. (p- -q) V (q-~r) 7. If Clayton pitches, the Dodgers win. r-P PV-r The Dodgers do not win. qur r- p Clayton does not pitch. 27. Earlier vP - q 5. If he doesn't have to get up at 3:00 A.M., he's ecstatic. "Poulo art nonT He's ecstatic. 21. (p- q) A (q-P) 22. (p / q) V (pvq) He doesn't have to get up at 3:00 A.M. P p v q p 6. "A mathematician is a device for turning coffee into theorems." (quote from Paul Erdos) 23. (-P V q) A (-P-q) 24. (r AP) - (rvq) You turn coffee into theorems. q AP r VP You are a mathematician. 25. (-P Ar) - (PV q) 26. (p- -q) V (q-~r) 7. If Clayton pitches, the Dodgers win. pv-r The Dodgers do not win. r-p Clayton does not pitch. 27. Earlier we showed how to analyze arguments using 8. If Josh plays, the opponent gets shut out. Euler diagrams. Refer to Example 5 in this section, The opponent does not get shut out. restate each premise and the conclusion using a quanti- fier, and then draw an Euler diagram to illustrate the Josh does not play. relationship. 9. "If you're going through hell, keep going." (quote from 28. Explain in a few sentences how to determine the state- Winston Churchill) ment for which a truth table will be constructed so that You're not going through hell. the arguments that follow in Exercises 29-38 can be analyzed for validity. Don't keep going. Determine whether each argument is valid or invalid. 10. "If you can't get rid of the skeleton in your closet, you'd best teach it to dance." (quote from George Bernard Shaw) 29. Joey loves to watch movies. If Terry likes to jog, then Joey does not love to watch movies. If Terry does not You can get rid of the skeleton in your closet. like to jog, then Carrie drives a school bus. Therefore, You'd best not teach it to dance. Carrie drives a school bus