26. A soft drink company produces three brands of soft drinks A,B and C . A market research group conducted a survey of 100 students and reported that 40 students buy brand B , 35 buy brand C and 10 buy only brand A, 15 students buy brands B and C , 10 students buy brands A and B , 5 students buy brands A and C but not brand B , 10 students buy brands B and C but not brand A . How many students (i) buy at least two brands of soft drinks ? (ii) Buy all three brands ? (iii) buy no soft drinks at all ? (iv) As a student what measures you take to spread awareness against soft drinks ?

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(BC)=15,n(AB)=10,nACB'=5,nBCA'=10Also, From the venn diagram, we have,n(A)=a+b+d+e=10a=-5n(B)=b+c+e+f=40c=20n(C)=d+e+f+g=35g=15n(AB)=b+e=10b=5nBC=e+f=15e=5nACB'=d=5nBCA'=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

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