37 1C Sets and Venn Diagrams DOES IT MAKE SENSE? 42. women and American presidents 43. teenagers and octogenarians Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. 7. The people who live in Chicago form a subset of those who rent apartments in Chicago. 8. All jabbers are wocks, so there must be no wocks that are not jabbers. 9, I counted an irrational number of students in my statistics class. 44. novels and mysteries 45-52: Categorical Propositions. For the given categorical propositions, do the following. a. If necessary, rephrase the statement in standard form. b. State the subject and predicate sets. c. Draw a Venn diagram for the proposition, and label all regions of the diagram. 10. I surveyed my class to find out whether students rode a bike on campus or not. Then I made a Venn diagram with one circle (inside a rectangle) to summarize the results. d. Based only on the Venn diagram (not on any other knowledge you have), answer the question that follows each proposition. 45. All kings are men. Can you conclude that some men are not kings? 11. My professor asked me to draw a Venn diagram for a categor- ical proposition, but I couldn't do it because the proposition was clearly false. 46. No carrots are fruit. Is it possible that some carrots are fruit? 47. Some surgeons are fishermen. Can you conclude that some fishermen are not surgeons? 12. I used a Venn diagram with three circles to show how many students on campus are vegetarians, Republicans, and/or women. 48. Every fish can swim. Can you conclude that some swimmers are not fish? BASIC SKILLS & CONCEPTS 49. Monks don't swear. Is it possible that some swearers are monks? 13-28: Classifying Numbers. Choose the first set in the list natural num- bers, whole numbers, integers, rational numbers, and real numbers that contains each of the following numbers. 50. Some days are Tuesdays. Based on this proposition, can you conclude that some days are not Tuesdays? 13. 888 14. -23 15. 3/4 51. Some sharpshooters are not men. Is it possible that at least one sharpshooter is a man? 16. -6/5 17. 3.414 18. 0 52. Some shortstops are blonds. Can you conclude that there are red-headed shortstops? 19. 7 20. V8 21. -45.12 22. V98 23. 7/4 24. -34/19.2 53-58: Venn Diagrams for Three Sets. Draw Venn diagrams with three overlapping circles (eight regions) for the following groups of three sets. Describe the members of each region, or state that a region has no 25. -123/79 26. -923.66 27. 7/129 28. 93,145,095 members. 29-36: Set Notation. Use set notation (braces) to write the members of the following sets, or state that the set has no members. You may use three dots (...) to indicate patterns. 53. women, Republicans, and chefs 54. hockey players, figure skaters, and men 29. The dates of July 55. poets, playwrights, painters 30. The odd numbers between and including 23 and 35 56. oceans, bodies of salt water, and bodies of fresh water 31. The states that share a border with the state of Mississippi 57. words that begin with t, nouns, and words with fewer than 5 letters 32. Every third number between 6 and 25, beginning with 6 33. The perfect squares between 10 and 40 58. teachers, swimmers, and tall people 59. Two-Way Table. An average of many different studies of handedness indicate that in a random sample of adults, 12 percent of men are left-handed and 9 percent of women are left-handed. (Assume the rest are right-handed.) Suppose you have a sample of 200 women and 150 men, in which the numbers of left-handed and right-handed people reflect the average percentages. Make a two-way table that shows the distribution you would find. 34. The states that begin with the letter K 35. Even numbers between 2 and 35 that are multiples of 3 36. The vowels of the English alphabet 37-44: Venn Diagrams for Two Sets. Draw Venn diagrams with two circles showing the relationship between the following pairs of sets. Provide an explanation of the diagram you draw. 11 37. teachers and women 60. Two-Way Table. According to exit polls from the 2016 Presidential election, Donald Trump received approximately 52% of the vote among white women, 4% of the vote among black women, 62% of the vote among white men, and 13% of the vote among black men. Show these data in a two-way table. 38. cage fighters and red-headed people 39. shirts and clothing 40. airliners and automobiles 41. poets and plumbers The nnot LICom 90000