Inclusion Exclusion Principle 200 Bostonians were surveyed regarding which rival teams they dislike. The 3 teams they were surveyed about were the Yankees, Lakers, and Canadiens: • 170 dislike the Yankees: • 143 dislike the Lakers: • 130 dislike the Canadiens: • 111 dislike the Yankees and Canadiens: • 120 dislike the Yankees and Lakers: • 99 dislike the Lakers and Canadiens; • 80 dislike all three teams. Use the inclusion-exclusion principle to answer the following questions, briefly describing your answer for each: I. How many people dislike either the Yankees, Lakers, or both? Answer: I. How many people dislike none of the three teams? Answer: III. How many people dislike just the Yankees? Answer: IV. How many people dislike both the Lakers and Canadiens, but not the Yankees? Hint 1: If you're getting caught up by "dislike" in the problem, you can change each instance to "like" and nothing about the answer will change. Hint 2: If you get stuck, draw a Venn diagram and color in the part you want to compute the cardinality of. Answer:

Inclusion Exclusion Principle 200 Bostonians were surveyed regarding which rival teams they dislike. The 3 teams they were surveyed about were the Yankees, Lakers, and Canadiens: • 170 dislike the Yankees: • 143 dislike the Lakers: • 130 dislike the Canadiens: • 111 dislike the Yankees and Canadiens: • 120 dislike the Yankees and Lakers: • 99 dislike the Lakers and Canadiens; • 80 dislike all three teams. Use the inclusion-exclusion principle to answer the following questions, briefly describing your answer for each: I. How many people dislike either the Yankees, Lakers, or both? Answer: I. How many people dislike none of the three teams? Answer: III. How many people dislike just the Yankees? Answer: IV. How many people dislike both the Lakers and Canadiens, but not the Yankees? Hint 1: If you're getting caught up by "dislike" in the problem, you can change each instance to "like" and nothing about the answer will change. Hint 2: If you get stuck, draw a Venn diagram and color in the part you want to compute the cardinality of. Answer:

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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Estimation

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Question

Inclusion Exclusion Principle
200 Bostonians were surveyed regarding which rival teams they dislike. The 3 teams they were surveyed
about were the Yankees, Lakers, and Canadiens:
. 170 dislike the Yankees;
• 143 dislike the Lakers:
• 130 dislike the Canadiens;
111 dislike the Yankees and Canadiens;
120 dislike the Yankees and Lakers;
• 99 dislike the Lakers and Canadiens;
• 80 dislike all three teams.
Use the inclusion-exclusion principle to answer the following questions, briefly describing your answer
for each:
I.
How many people dislike either the Yankees, Lakers, or both?
Answer:
I.
How many people dislike none of the three teams?
Answer:
II.
How many people dislike just the Yankees?
Answer:
IV.
How many people dislike both the Lakers and Canadiens, but not the Yankees? Hint 1: If you're
getting caught up by "dislike" in the problem, you can change each instance to "like" and
nothing about the answer will change. Hint 2: If you get stuck, draw a Venn diagram and color in
the part you want to compute the cardinality of.
Answer:

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