Thirty-eight cities were researched to determine whether they had a professional sports​ team, a​ symphony, or a​ children's museum. of these cities, 21 had a professional sports team, 20 had a​ symphony, 17 had a​ children's museum, 14 had a professional sports team and a​ symphony, 10 had a professional sports team and a​ children's museum, 10 had a symphony and a​ children's museum, and 6 had all three activities. How many of the cities surveyed had only a professional sports​ team?

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

10 had a symphony and a​ children's museum,

This means that:

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

14 had a professional sports team and a​ symphony

21 had a professional sports team

This means that:

In which (A - B - C) represents the cities which had only a sports team. So

3 of the cities surveyed had only a professional sports​ team.

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step-by-step explanation: