EXERCESES ., .. r. x. '., a . _ . _. .. . 5., . to, *- w a, . . . - 2 'I ."" \"'..'" ' '3 0 Practice by Example For Exercises ll2.lind each union or Intersection. Let A = [2, 5],]? = [5,7, 9|, C 2 tr I .r Is an odd number less tlmn 9]. and D = {r l .r is an even number less than 9]. summer @4 u n 2. A u c @A u n ' lz'i' m... M 1-: u ' . \" . . ' ' , 7 3 ) , 7 '93} Mp 4 n U( @t u I 6 c u 1) Example 2 @A n I: s. A n (T @A n D \"\"9\" "V 7\"" 10. H n c 11. 11 n I.) 12. C n I) Example 3 For Exercises 13-16. drew a Venn diagram to represent the union and Intersection ing!) NY 7415) of the given sets. Wt Alex has cats. rabbits. and sh as pets. Becky has cats and dogs. Cory has cats. birds. tish.and turtles. Let A = {cats rabbits. sh]. B = [cats.dogs].and C = leats. birds, sh. turtles]. .Let X = [x | x is a letter in the word ALGEBRA}, Y = {y l y is a letter in the word GEOMETRY], and Z = [ z I z is a letter in the word CALCULUS}. @Let P = [.r ix is a prime number less than 10]. C = {l. 2. 3. 4. 5. 6. 7. 8. 9. '10]. and O = {a | u is an odd number less than 1.0]. @Let l. = {a. b. c. 1,2.3, horse. Cow. pig], M = [-1,(). Lb. y. pig. duck. A]. and N = {c.3,duck,A]. Example Li 17. 0f 75 people with cell phones. 42 take pictures with their cell phone and 36 use {page NY 745) their cell phone to take pictures and send text messages. How many use their phones to send text messages? 18. Of 100 people in a band. 70 members said they play a sport and 50 members play a sport and take music lessons. How many take music lessons? @ An ice cream shop owner surveys 200 people who eat chocolate and vanilla ice cream. If 154 people like both avors, and 196 people like vanilla. how many people like chocolate? 9 Apply Your Skills @Reaaeninq Find two setsA and B such that A U B = \26. Of students surveyed. 80 had visited the planetarium. 75 had visited Ellis Island, and 65 had been to Niagara Falls. 30 students went to both the planetarium and Ellis Island. 25 went to the planetarium and Niagara Falls, and 10 went to Ellis Island and Niagara Falls. Only 5 went to all three. a. How many students went only to the planetarium? b. How many students went only to Niagara Falls? c. How many students did not go to Ellis Island but went to the planetarium or Niagra Falls? d. How many total students were surveyed? The planetarium at the American 27. Open-Ended Find two sets A and B such that A U B = (1, 2. 3. 4, 5) eum of Natur New York City is spherical. and An B = 0. 28. Let P = { x x is a prime number) and Q = (x 1 x is a multiple of 6). Describe the intersection of P and Q. C Challenge For Exercises 29-32, write each set in roster notation. Let X = (a, c, e, g, i), Y = (b, c, e, f), and Z = (b, d, f). 29. n (XUY) 30. ZU ( XnY) 31. YU (Zn X) 32. ( YU Z) n X 33. Critical Thinking Is the equality (A U B) n C = A U (Bn C) always, sometimes. or never true? Justify your answer. NY REGENTS Decpee 86998. Test Prep Multiple Choice 34 Consider the set D of all numbers in the interval (-co, 5). What is the complement of D? A. (-0o, - 5) B. [5, + 00) C. ( -0o, 5 ) D. (5 , +00) 35. Set X = {x | x is a factor of 12) and set Y = {y | y is a factor of 16). Which set represents X n Y? F. e G. {0, 1, 2, 4) H. {1, 2, 4} J. {1, 2, 3, 4, 6, 8, 12, 16} Short Response 36. Let the universal set U represent the integers from 1 to 10. Use the subsets of M = (x | x is a factor of 8), and N = {1, 4, 6, 7, 10} to find the complement of M U N. Mixed Review Lesson NY-1 Classify each as qualitative or quantitative data. 37. number of movies watched 38. favorite pizza toppings 39. colors of passing cars 40. SAT math scores Lesson NY-2 Find the median, the first quartile, and the third quartile of each data set. 41. 3 5 8 2 11 15 13 42. 17 20 11 34 91 12 29 43. 105 121 151 89 93 141 Lesson NY-4 Union and Intersection of Sets NY 747