Let’s go step by step using the Venn diagram numbers:
We are given:
- Only Tennis (not Swimming):
6
- Both Tennis and Swimming:
18
- Only Swimming (not Tennis):
17
- Neither Tennis nor Swimming (outside both circles):
5
Total students = 6 + 18 + 17 + 5 =
46
Now let’s answer each question one by one.
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1) How many students like Tennis or Swimming?
This means: anyone in Tennis circle OR Swimming circle (including both).
= Only Tennis + Both + Only Swimming
= 6 + 18 + 17 =
41
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2) How many students do not like Tennis?
These are people outside the Tennis circle:
= Only Swimming + Neither
= 17 + 5 =
22
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3) How many students do not like either Tennis or Swimming?
That’s the number outside both circles:
5
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4) How many students like Swimming?
Everyone in the Swimming circle:
= Only Swimming + Both
= 17 + 18 =
35
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5) How many students do not like Swimming?
Outside the Swimming circle:
= Only Tennis + Neither
= 6 + 5 =
11
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6) How many students like Tennis?
Everyone in the Tennis circle:
= Only Tennis + Both
= 6 + 18 =
24
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7) How many students like both Tennis and Swimming?
The overlapping part:
18
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8) How many students only like Tennis?
Only in Tennis, not in Swimming:
6
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9) How many students only like Swimming?
Only in Swimming, not in Tennis:
17
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10) How many students do not like both Tennis and Swimming?
This is tricky wording. “Do not like both” usually means they don’t like *at least one* — but in math problems like this, it often means “do not like *either*” — which is the same as question #3.
But let’s check carefully.
Actually, “do not like both” can be ambiguous. But looking at context:
In logic, “do not like both A and B” = NOT (like A AND like B) → so everyone EXCEPT those who like both.
So total students minus those who like both:
Total = 46
Like both = 18
→ Do not like both = 46 - 18 =
28
Wait — let’s verify with another way:
People who do NOT like both =
- Like only Tennis: 6
- Like only Swimming: 17
- Like neither: 5
Total = 6 + 17 + 5 =
28
Yes! So “do not like both” means they are NOT in the intersection — so 28.
BUT — sometimes in elementary worksheets, “do not like both” might be misinterpreted. However, based on standard interpretation in set theory:
“Do not like both” = complement of “like both” → so 28.
However, let’s double-check question #10 vs #3.
Question #3: “do not like either” → that’s clearly 5.
Question #10: “do not like both” → should mean not liking the combination → so 28.
Yes, that makes sense.
Alternatively, if the worksheet meant “do not like either”, they would have said “either” again. Since they used “both”, it’s likely referring to the intersection.
So final answer for #10:
28
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✔ All answers verified.
Final Answer:
1) 41
2) 22
3) 5
4) 35
5) 11
6) 24
7) 18
8) 6
9) 17
10) 28
Parent Tip: Review the logic above to help your child master the concept of set worksheet.
