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a class of 40 students are taking the following. 18 are taking math 20 are taking english 15 are taking chemistry 4 are taking chemistry and english 6 are taking math and english 8 are taking chemistry and math 2 are taking alll subject how many are taking english only? how many are taking math only? how many are taking che,mistry only? how many are not taking of the three?

Respuesta :

Using Venn sets, it is found that:

  • 12 students are taking English only.
  • 6 students are taking Math only.
  • 5 students are taking Chemistry only.
  • 3 students are not taking any of the classes.

What are the Venn Sets?

For this problem, we consider the following sets:

  • Set A: students taking Math.
  • Set B: students taking English.
  • Set C: students taking Chemistry.

2 are taking all subjects, hence:

(A ∩ B ∩ C) = 2.

8 are taking chemistry and math, hence:

(A ∩ C) + (A ∩ B ∩ C) = 8.

(A ∩ C) = 6.

6 are taking math and english, hence:

(A ∩ B) + (A ∩ B ∩ C) = 6.

(A ∩ B) = 4.

4 are taking chemistry and english, hence:

(B ∩ C) + (A ∩ B ∩ C) = 4.

(B ∩ C) = 2.

15 are taking chemistry, hence:

C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 15.

C + 6 + 2 + 2 = 15.

C = 5.

20 are taking english, hence:

B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 20

B + 4 + 2 + 2 = 20

B = 12.

18 are taking math, hence:

A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 18

A + 4 + 6 + 2 = 18

A = 6.

There is a total of 40 students, hence:

None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 40.

None + 6 + 12 + 5 + 4 + 6 + 2 + 2 = 40.

None + 37 = 40.

None = 3.

Hence:

  • 12 students are taking English only.
  • 6 students are taking Math only.
  • 5 students are taking Chemistry only.
  • 3 students are not taking any of the classes.

More can be learned about Venn sets at brainly.com/question/24388608

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