Question

For any two sets $A$ and $B,n(A)=25,n(B)=13$, $A\cap B\ne \varphi$ and $B\not\subset A$. The maximum possible value of $n(A\Delta B)$___

Answer 1

Answer: 36

For the maximum value of $n(A\Delta B)$, $n(A\cap B)$ should be minimum.
The minimum value of $n(A\cap B)=1$,
$(\because n(A\cap B)\ne 0).$
$\therefore n(A\Delta B)=n(A\cup B)-n(A\cap B)=n(A)+n(B)-2[n(A\cap B)]=25+13-2=36$