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Sagot :
Answer:
3 of the cities surveyed had only a professional sports team.
Step-by-step explanation:
We solve this question treating these as Venn sets.
I am going to say that:
Set A: professional sports team.
Set B: Symphony.
Set C: Children's museum.
We start building from the intersection of these three.
6 had all three activities.
This means that [tex]A \cap B \cap C = 6[/tex]
10 had a symphony and a children's museum,
This means that:
[tex](B \cap C) + (A \cap B \cap C) = 10[/tex]
[tex](B \cap C) + 6 = 10[/tex]
[tex](B \cap C) = 4[/tex]
That is, 4 have only the symphony and children's museum, while 6 have all three.
10 had a professional sports team and a children's museum
[tex](A \cap C) + (A \cap B \cap C) = 10[/tex]
[tex](A \cap C) + 6 = 10[/tex]
[tex](A \cap C) = 4[/tex]
14 had a professional sports team and a symphony
[tex](A \cap B) + (A \cap B \cap C) = 14[/tex]
[tex](A \cap B) + 6 = 14[/tex]
[tex](A \cap B) = 8[/tex]
21 had a professional sports team
This means that:
[tex](A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 21[/tex]
In which (A - B - C) represents the cities which had only a sports team. So
[tex](A - B - C) + 8 + 4 + 6 = 21[/tex]
[tex](A - B - C) = 3[/tex]
3 of the cities surveyed had only a professional sports team.
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