Dear student Let A,B and C denote the set of students who have taken brand A,B,C respectively So, n(B)=40,n(C)=35,n(A)=10,n(B∩C)=15,n(A∩B)=10,nA∩C∩B'=5,nB∩C∩A'=10Also, From the venn diagram, we have,n(A)=a+b+d+e=10⇒a=-5n(B)=b+c+e+f=40⇒c=20n(C)=d+e+f+g=35⇒g=15n(A∩B)=b+e=10⇒b=5nB∩C=e+f=15⇒e=5nA∩C∩B'=d=5nB∩C∩A'=f=101) Required number of students=b+d+f+e=5+5+10+5=252) Required number of students=100-a+b+c+d+e+f+g=-5+5+20+5+5+10+15=553)Required number of students=100-55=45 Regards

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Let A, B and C denote the set of students who have taken brand A, B, C respectively . So, n (B) = 40, n (C) = 35, n (A) = 10, n (B \cap C) = 15, n (A \cap B) = 10, n (A \cap C \cap B') = 5, n (B \cap C \cap A') = 10 Also, From the venn diagram, we have, n (A) = a + b + d + e = 10 \Rightarrow a = - 5 n (B) = b + c + e + f = 40 \Rightarrow c = 20 n (C) = d + e + f + g = 35 \Rightarrow g = 15 n (A \cap B) = b + e = 10 \Rightarrow b = 5 n (B \cap C) = e + f = 15 \Rightarrow e = 5 n (A \cap C \cap B') = d = 5 n (B \cap C \cap A') = f = 10 1) Required number of students = b + d + f + e = 5 + 5 + 10 + 5 = 25 2) Required number of students = 100 - (a + b + c + d + e + f + g) = (- 5 + 5 + 20 + 5 + 5 + 10 + 15) = 55 3) Required number of students = 100 - 55 = 45

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