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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