i. non-negativity:-
value of \(\frac{\left|X\cap Y\right|}{\left|X\cup Y\right|}\) ranges from 0 to 1, with 1 being the maximum value.This is because union of two sets is always greater than or equal to the intersection of the sets.The equality exists when both sets are the same.
Therefore, \(JD\left(X,Y\right)=1-\frac{\left|X\cap Y\right|}{\left|X\cup Y\right|}\ is\ always\ greater\ than\ 0\).Thus, the function satisfies the property of non-negativity.