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d If the (8). disjoint s of and 2 is model wing 42. How many 5-digit ZIP code numbers are possible? How many of these numbers contain no repeated digits? 43. In Example 3, does it make any difference in which order the selection operations are performed? That is, if we select a jacket color first and then select a size, are there as many combined choices available as selecting a size first and then a color? Justify your answer using tree diagrams and the multiplication principle. 44. Explain how three sets, A, B, and C, can be related to each other in order for the following equation to hold true (Venn diagrams may be helpful): n(AUBUC) n(A) + n(B) + n(C) (ANC)-(BOC). Problems 45-48 refer to the following Venn diagram 45. Which of the numbers x, y, z, or w must equal 0 if BCA? 46. Which of the numbers x, y. 2. or w must equal 0 if A and B are disjoint? 47. Which of the numbers x, y, c. or w must equal 0 AUB-ANB? 48. Which of the numbers r.y.tor w must equal 0 if AUB-UT 49. A group of 75 people includes 32 who play tennis, 37 who play golf, and 8 who play both tennis and golf. How many people groop play neither sport? 50. A clan of 16 who play clades 13 who play the piano and 3 who play both the piano and the

d If the (8). disjoint s of and 2 is model wing 42. How many 5-digit ZIP code numbers are possible? How many of these numbers contain no repeated digits? 43. In Example 3, does it make any difference in which order the selection operations are performed? That is, if we select a jacket color first and then select a size, are there as many combined choices available as selecting a size first and then a color? Justify your answer using tree diagrams and the multiplication principle. 44. Explain how three sets, A, B, and C, can be related to each other in order for the following equation to hold true (Venn diagrams may be helpful): n(AUBUC) n(A) + n(B) + n(C) (ANC)-(BOC). Problems 45-48 refer to the following Venn diagram 45. Which of the numbers x, y, z, or w must equal 0 if BCA? 46. Which of the numbers x, y. 2. or w must equal 0 if A and B are disjoint? 47. Which of the numbers x, y, c. or w must equal 0 AUB-ANB? 48. Which of the numbers r.y.tor w must equal 0 if AUB-UT 49. A group of 75 people includes 32 who play tennis, 37 who play golf, and 8 who play both tennis and golf. How many people groop play neither sport? 50. A clan of 16 who play clades 13 who play the piano and 3 who play both the piano and the

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with problems 42 and 50. Thank you so much
troduction to X reader2.yuzu.com/reader/books/9780136470809/pageid/394 ! 1 25. n(A)=70, n(B) = 90, n(ANB) 30, n(U) - 200 26. n(A) 55. (B) 65, n(ANB) 35; n(U) = 100 27. n(A)= 45, n(B) 55. n(AUB) 80, n(U)= 100 28. n(A) 80, n(B) = 70, 29. n(A) 15. n(B') n(AUB) = 110, n(U) = 200 24, mpaka 32. (U) = 90 moy www n(AUB) Mor B 30. n(A) 81, n(B) = 90, (A'B')-63, n(U) 180. 31. (A) 110, n(B) = 145. (AUB) 255. n(U) = 300 32. (A) 175, n(B) 125, (AUB)- 300, (U)= 300 FI Yuzu Reader: MyLab Math for X + In Problems 33 and 34, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. 33. (A) If A or B is the empty set, then A and B are disjoint. (B) If A and B are disjoint, then A or B is the empty set. 34. (A) If A and B are disjoint, then n(AB) n(A) + n(B) (B) If n(AUB) = n(A) + n(B), then A and B are disjoint. 35. A particular new car model is available with 5 choices of color, 3 choices of transmission, 4 types of interior, and 2 types of engine. How many different variations of this model are possible? 36. A delicatessen serves meat sandwiches with the following options: 3 kinds of bread, 5 kinds of meat, and lettuce or sprouts. How many different sandwiches are possible, assum @ 2 stala F2 # 3 80 F3 $ 4 a F4 42. How many 5-digit ZIP code numbers are possible? How many of these numbers contain no repeated digits? 43. In Example 3, does it make any difference in which order the selection operations are performed? That is, if we select a jacket color first and then select a size, are there as many combined choices available as selecting a size first and then a color? Justify your answer using tree diagrams and the multiplication principle. % 5 44. Explain how three sets, A, B, and C, can be related to each other in order for the following equation to hold true (Venn diagrams may be helpful): n(AUBUC) = n(A) + n(B) + n(C) n(ANC) n(BOC) CProblems 45-48 refer to the following Venn diagram. 45. Which of the numbers x, y, z, or w must equal 0 if BCA? 46. Which of the numbers x, y, z, or w must equal 0 if A and B are disjoint? 47. Which of the numbers x, y, z, or w must equal 0 if AUB ANB? 48. Which of the numbers x, y, z, or w must equal 0 ir AUB=U? 49. A group of 75 people includes 32 who play tennis, 37 who play golf, and 8 who play both tennis and golf. How many people in the group play neither sport? 50. A class of 30 music students includes 13 who play the piano, 16 who play the guitar, and 5 who play both the piano and the guitar. How many students in the class play neither instrument? #1 of 100 43 ↓ X ^ 6 S F6 & 7 F7 * 8 D
Transcribed Image Text:troduction to X reader2.yuzu.com/reader/books/9780136470809/pageid/394 ! 1 25. n(A)=70, n(B) = 90, n(ANB) 30, n(U) - 200 26. n(A) 55. (B) 65, n(ANB) 35; n(U) = 100 27. n(A)= 45, n(B) 55. n(AUB) 80, n(U)= 100 28. n(A) 80, n(B) = 70, 29. n(A) 15. n(B') n(AUB) = 110, n(U) = 200 24, mpaka 32. (U) = 90 moy www n(AUB) Mor B 30. n(A) 81, n(B) = 90, (A'B')-63, n(U) 180. 31. (A) 110, n(B) = 145. (AUB) 255. n(U) = 300 32. (A) 175, n(B) 125, (AUB)- 300, (U)= 300 FI Yuzu Reader: MyLab Math for X + In Problems 33 and 34, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. 33. (A) If A or B is the empty set, then A and B are disjoint. (B) If A and B are disjoint, then A or B is the empty set. 34. (A) If A and B are disjoint, then n(AB) n(A) + n(B) (B) If n(AUB) = n(A) + n(B), then A and B are disjoint. 35. A particular new car model is available with 5 choices of color, 3 choices of transmission, 4 types of interior, and 2 types of engine. How many different variations of this model are possible? 36. A delicatessen serves meat sandwiches with the following options: 3 kinds of bread, 5 kinds of meat, and lettuce or sprouts. How many different sandwiches are possible, assum @ 2 stala F2 # 3 80 F3 $ 4 a F4 42. How many 5-digit ZIP code numbers are possible? How many of these numbers contain no repeated digits? 43. In Example 3, does it make any difference in which order the selection operations are performed? That is, if we select a jacket color first and then select a size, are there as many combined choices available as selecting a size first and then a color? Justify your answer using tree diagrams and the multiplication principle. % 5 44. Explain how three sets, A, B, and C, can be related to each other in order for the following equation to hold true (Venn diagrams may be helpful): n(AUBUC) = n(A) + n(B) + n(C) n(ANC) n(BOC) CProblems 45-48 refer to the following Venn diagram. 45. Which of the numbers x, y, z, or w must equal 0 if BCA? 46. Which of the numbers x, y, z, or w must equal 0 if A and B are disjoint? 47. Which of the numbers x, y, z, or w must equal 0 if AUB ANB? 48. Which of the numbers x, y, z, or w must equal 0 ir AUB=U? 49. A group of 75 people includes 32 who play tennis, 37 who play golf, and 8 who play both tennis and golf. How many people in the group play neither sport? 50. A class of 30 music students includes 13 who play the piano, 16 who play the guitar, and 5 who play both the piano and the guitar. How many students in the class play neither instrument? #1 of 100 43 ↓ X ^ 6 S F6 & 7 F7 * 8 D
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