This question is from the chapter : sets

Of the 24 students in a class , 18 like to play basketball and 12 like to play volleyball . Find the largest possible number of students who likes to play both ?

I actually know the answer and working for this but I just wanted to ask you a doubt in the working

The working is :
n(BnV) is largest when V≤B
Whereas the answer will be 12

so my question is why is it largest when V≤B
The answer can be 24 right as it is asking how many people maximum may like to play both . So it can be 24 right ?

pls explain the answer briefly

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Solution

If we want to maximize those who like both, we have to maximize the value in the intersection. So, we have to minimize the value of the union.
This is possible only when V≤B
since V is small set compared to B

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If we want to maximize those who like both, we have to maximize the value in the intersection. So, we have to minimize the value of the union. This is possible only when V≤B since V is small set compared to B

If we want to maximize those who like both, we have to maximize the value in the intersection. So, we have to minimize the value of the union.
This is possible only when V≤B
since V is small set compared to B