**Answer:**

(a) = 13

(b) = 8

(c) = 5

**Step-by-step explanation:**

Addition **theorems** on **sets ** are

**Theorem 1** :

n(AuB) = n(A) + n(B) - n(AnB)

**Theorem 2 **:

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

Total number of students in the school is not given

so let there are 60 students in the school

using theorem 2

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

60 = 40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)

60 +73 -120 = n(AnBnC)

13 = n(AnBnC)

therefore, there are total 13 students who take all three subjects

Number of students who had taken only Mathematics =

n(A) - n(AnB) - n(AnC) + n(AnBnC)

40 - 20 - 25 + 13

53 - 45 = 8 students

Number of students who had taken only Physics =

n(B) - n(BnA) - n(BnC) + n(AnBnC)

42 - 20 - 28 + 13

53 - 48 = 5 students

learn more about **sets **and **vein diagrams **at

brainly.com/question/2332158

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