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Consider the following data for 120 mathematics students at a college concerning the languages French, German, and Russian:
65 study French, 45 study German,
42 study Russian , 20 study French and German,
25 study French and Russian,
15 study German and Russian.
8 study all three languages.
Determine how many students study exactly 1 subject and fill the correct numbers of students in each eight region of Venn diagram shown in figure.

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Answer:

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The Venn diagram for given situation is as shown below.

The number of students who study exactly one subject = 56

What is set?

"It is a collection of well-defined elements"

What is Venn diagram?

"It is a pictorial representation that uses circles to show the relationships among sets."

For given example,

We have been given the data for 120 mathematics students at a college concerning the languages French, German, and Russian

Let set A, B and C represents the number of students who study French, German and Russian respectively.

⇒ n(A) = 65

⇒ n(B) = 45

⇒ n(C) = 42

20 study French and German

⇒ n(A ∩ B) = 20

25 study French and Russian,

⇒ n (A ∩ C) = 25

15 study German and Russian.

⇒ n(B ∩ C) = 15

8 study all three languages.

⇒ n(A ∩ B ∩ C) = 8

So, the Venn diagram for given situation is shown below.

Now, we find the number of students who study exactly one subject.

28 students study French only, 18 students study German only and 10 students study Russian only.

So, the total number of students who study exactly one subject is,

28 + 18 + 10 = 56

Therefore, 56 students study exactly one subject

Learn more about Venn diagram here:

https://brainly.com/question/1605100

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