In a class, there are 200 students, at least 140 of students like Maths(Set A), at least 150 like Science(Set B) and at least 160 like English(Set C). What is the minimum and maximum number of students who like all three subjects?
I am able to find the maximum value that an intersection of three set can hold. My approach is, Maximum value for set A,B,C can be 200. So when they completely overlap i.e Each student among 200 student likes all three subject that maximum value of (A ∩ B ∩ C) can be 200.
But I am not able to figure out the minimum value of (A ∩ B ∩ C).
Approach that I tried finding the minimum value of (A ∩ B ∩ C).
As $(A \cup B \cup C)=A+B+C-(A ∩ B)-(A ∩ C)-(B ∩ C)+(A ∩ B ∩ C)$ Considering the minimum value of A,B,C then the Maximum value of $(A ∩ B)=(A ∩ C)=(B ∩ C)$ should be the size of set with minimum value of student i.e $140$ so $(A ∩ B ∩ C)=-140-150-160+3*140+200$ But this approach is not giving the right answer?
What I am doing wrong?
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