Only 29,30,34,36,37,38,39

Level 2 FOR WANDERWAS LOST Use a symbolic argument in Problems 29-32 to determine if the Mo FOR WANT OF FOR WANT OF A SHOE THE RIDER argument is valid or invalid. THE HORSE W WAS LOST . " 29. All mathematicians are eccentrics. All eccentrics are rich. Therefore, all mathematicians are rich. 30. No students are enthusiastic. "FOR WANT OF KNOW WHAT GOOD YES . You are enthusiastic. THE BATTLE THAT MEANS , WAS LOST . " Ton Therefore, you are not a student. 31. If the crime occurred after 4:00 A.M., then Smith could not have done it. If the crime occurred at or before 4:00 A.M., then Jones could not have done it. Reprinted with special permission. King Features Syndicate The crime involved two persons, if Jones did not commit the YOU DIE WELL, I'M NAILS GET THEM crime. SARGE TO CARE ABOUT Therefore, if Smith committed the crime, it involved two THINGS persons. 32. (Let x be an integer and y a nonzero integer for this argument.) 9-15 If Q is a rational number, then Q = y, where ; is a reduced fraction. Q # , where , is a reduced fraction. 45. If I eat that piece of pie, I will get fat. I will not get fat. Therefore, Q is not a rational number. 46. If 2 divides a positive integer N and if N is greater than 2, then 33. Prove [(p - q) A p] - q by constructing a truth table. What N is not a prime number. is the name we give to this type of reasoning? N is a prime number. 34. Prove [(p- q) A ~q]- ~p by constructing a truth table. 47. If we win first prize, we will go to Europe. What is the name we give to this type of reasoning? If we are ingenious, we will win first prize. 35. Show that [(p - q) A (p-r)]- (q->r) is an invalid We are ingenious. argument by constructing a truth table. What is the name of 48. If I am tired, then I cannot finish my homework. this fallacy? If I understand the homework, then I can finish 36. Prove that [(p - q) A ~p] - ~q is an invalid argument. my homework. What is the name of this fallacy? Level 3 In Problems 37-48, form a valid conclusion, using all the premises given for each argument. Give reasons. HISTORICAL QUEST In Problems 49-52, write a valid conclusion. These problems were written by Charles Dodgson, better known 37. If you learn mathematics, then you are intelligent. as Lewis Carroll. You might wish to read the Historical Note and If you are intelligent, then you understand human nature. Example 5 in this section. 38. If I am idle, then I become lazy. 49. Babies are illogical. I am idle. Nobody is despised who can manage a crocodile. 39. If we go to the concert, then we are enlightened. Illogical persons are despised. We are not enlightened 50. All hummingbirds are richly colored. 40. If you climb the highest mountain, then you feel great. No large birds live on honey. If you feel great, then you are happy. Birds that do not live on honey are dull in color. 51. No ducks waltz. 41. a = 0 orb = 0 No officers ever decline to waltz. a + 0 All my poultry are ducks. 42. If a . b = 0, then a = 0 or b = 0. 52. Everyone who is sane can do logic. a . b = 0 No lunatics are fit to serve on a jury. 43. If we interfere with the publication of false information, we are None of your sons can do logic. guilty of suppressing the freedom of others. We are not guilty of suppressing the freedom of others. 53. If the government awards the contract to Airfirst Aircraft Company, then Senator Firstair stands to earn a great deal of money. 44. If a nail is lost, then a shoe is lost. If Airsecond Aircraft Company does not suffer financial setbacks, If a shoe is lost, then a horse is lost. then Senator Firstair does not stand to earn a great deal of If a horse is lost, then a rider is lost. money. If a rider is lost, then a battle is lost. The government awards the contract to Airfirst Aircraft If a battle is lost, then a kingdom is lost. Company