142 CHAPTER 3 Logic In Exercises 43– 48, write the converse, inverse, and contrapositive of the statement in sentence form. 43. If you got straight A’s, then you are on the president’s list. * 44. If it is windy, then we go sailing. * 45. If Kohl’s has a sale, then I go shopping. * 46. If I write a haiku, then you write a sonnet. * 47. If the menu includes calzones, then I do not stay on my diet. * 48. If Grandma is not available to babysit, then we cannot go to the movie. * In Exercises 49–54, write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false. 49. If a natural number is divisible by 14, then the natural number is divisible by 7. If a natural number is not divisible by 7, then the natural number is not divisible by 14. True. 50. If the quadrilateral is a parallelogram, then the opposite sides are parallel. If the opposite sides are not parallel, then the quadrilateral is not a parallelogram. True. 51. If a natural number is divisible by 3, then the natural number is divisible by 6. If a natural number is not divisible by 6, then the natural number is not divisible by 3. False. 52. If the number is not a natural number, then the number is not a positive number. If the number is a positive number, then the number is a natural number. False. 53. If two lines do not intersect in at least one point, then the two lines are parallel. If two lines are not parallel, then the two lines intersect in at least one point. True. 54. If two lines are perpendicular, then the two lines are not parallel. If two lines are parallel, then the two lines are not perpendicular. True. In Exercises 55– 68, determine which, if any, of the three statements are equivalent (see Example 13). 55. a) If the pie is apple, then I will have a piece of pie. b) If I have a piece of pie, then the pie is apple. c) I do not have a piece of pie or the pie is apple. b) and c) are equivalent. 56. a) If the dress is a Prada, then it is not a Gucci. b) It is not true that the dress is a Prada and it is not a Gucci. c) The dress is not a Prada or it is a Gucci. b) and c) are equivalent 57. a) The shoes are not on sale but the purse is on sale. b) If the shoes are not on sale then the purse is not on sale. c) It is false that the shoes are on sale or the purse is not on sale. a) and c) are equivalent. 58. a) LeBron did not play for the Dragonflies or Giannis did not play for the Robots. b) If LeBron played for the Dragonflies, then Giannis played for the Robots. c) It is not true that Giannis played for the Robots and LeBron did not play for the Dragonflies. None are equivalent 59. a) We do not go hiking or we go fishing. b) If we go hiking, then we do not go fishing. c) If we go fishing, then we do not go hiking. b) and c) are equivalent. 60. a) If Tim is the director then Johnny is the actor. b) Tim is not the director or Johnny is the actor. c) It is false that Tim is the director and Johnny is not the actor. a), b), and c) are equivalent. 61. a) Today is Monday and the garbage gets picked up. b) If the garbage gets picked up, then today is not Monday. c) The garbage does not get picked up or today is not Monday. b) and c) are equivalent. 62. a) Akemi plays Star Stable if and only if she plays Just Dance. b) If Akemi plays Star Stable, then she plays Just Dance, and if Akemi plays Just Dance, then she plays Star Stable. c) Akemi does not play Star Stable and she does not play Just Dance. a) and b) are equivalent *See Instructor Answer Appendix Iakov Filimonov/123RF Brent Hofacker/123RF
RkJQdWJsaXNoZXIy NjM5ODQ=