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Maximum and minimum size of the join of two relations

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I am confused about this problem:
Relation A -> m tuples
Relation B -> n tuples

What is the maximum and minimum size of natural join?
According to this,  maximum can be -> min(m,n) and minimum can be 0.
I want to know if it is asked that what is maximum and minimum size on join operation (not natural join) will the answer get changed?

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As the natural join take the common attribute and combines according to them lets . take a relation R(a,b,c) an a relation S(a,p,q) such that no value of a of r is repeated in the attribute A of relation s. so natural join will take the cross product and will search where R.a=S.a so nothing will be selected and zero tupples will be returned, while if we does not have common attributes then it take the cross product an as it now does not which to compare as there is no common attribute it, stops there only providing you the cartesian product.
so minimum - zero

max- R*S.

and the min max will change according to join or the constraint
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