Step-by-step explanation:
the max. value is when the smaller set (A) is completely contained in the larger set (B).
then n(A n B) is n(A) = 50.
the set intersection between A and B cannot get bigger than that. or A gets bigger ...
after all, the intersection means it is a set of all elements that exist in BOTH sets.
but then there must be other elements besides A and B in the universal set too, because n(universal set) = 96, and n(A u B) would be only 60.
the min. value could be the empty set or 0. but because n(universal set) = 96, and n(A) + n(B) = 110 and larger than 96, it means that there have to be some shared elements. at least 110 - 96 = 14 elements.
in this case there cannot be other elements in the universal set than A and B. and n(universal set) = n(AuB) = 96.
