Problem Analysis:
The Venn diagram provided shows the preferences of students for Tennis and Swimming. The regions are labeled as follows:
-
Tennis only: 5 students
-
Both Tennis and Swimming: 18 students
-
Swimming only: 17 students
-
Neither Tennis nor Swimming: 6 students
We need to answer 10 questions based on this Venn diagram. Let's solve each question step by step.
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Question 1: How many students like Tennis or Swimming?
To find the total number of students who like either Tennis or Swimming (or both), we sum the students in all regions except the "Neither" region:
- Tennis only: 5
- Both Tennis and Swimming: 18
- Swimming only: 17
Total = 5 + 18 + 17 = 40
Answer: 40
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Question 2: How many students do not like Tennis?
Students who do not like Tennis are those who:
- Like only Swimming: 17
- Like neither Tennis nor Swimming: 6
Total = 17 + 6 = 23
Answer: 23
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Question 3: How many students do not like either Tennis or Swimming?
This is the number of students in the "Neither" region:
- Neither Tennis nor Swimming: 6
Answer: 6
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Question 4: How many students like Swimming?
Students who like Swimming include those who:
- Like only Swimming: 17
- Like both Tennis and Swimming: 18
Total = 17 + 18 = 35
Answer: 35
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Question 5: How many students do not like Swimming?
Students who do not like Swimming are those who:
- Like only Tennis: 5
- Like neither Tennis nor Swimming: 6
Total = 5 + 6 = 11
Answer: 11
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Question 6: How many students like Tennis?
Students who like Tennis include those who:
- Like only Tennis: 5
- Like both Tennis and Swimming: 18
Total = 5 + 18 = 23
Answer: 23
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Question 7: How many students like both Tennis and Swimming?
This is the number of students in the intersection of the two circles:
- Both Tennis and Swimming: 18
Answer: 18
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Question 8: How many students only like Tennis?
This is the number of students in the "Tennis only" region:
- Tennis only: 5
Answer: 5
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Question 9: How many students only like Swimming?
This is the number of students in the "Swimming only" region:
- Swimming only: 17
Answer: 17
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Question 10: How many students do not like both Tennis and Swimming?
This is the number of students who like neither activity:
- Neither Tennis nor Swimming: 6
Answer: 6
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Final Answers:
1.
40
2.
23
3.
6
4.
35
5.
11
6.
23
7.
18
8.
5
9.
17
10.
6
Boxed Final Answer:
\[
\boxed{40, 23, 6, 35, 11, 23, 18, 5, 17, 6}
\]
Parent Tip: Review the logic above to help your child master the concept of sets and venn diagram worksheet.
