Let n(A) = m and n(B) = n, if the number of subsets of A is 56 more than of subsets of B, then m + n is equal to

Since, total possible subsets of sets A and B are 2^m and 2ⁿ, respectively.
According to given condition,
$\begin{array}{l}{2}^{\mathrm{m}}-2^{\mathrm{n}}=56\\ \Rightarrow 2^{\mathrm{n}}\left(2^{\mathrm{m}-\mathrm{n}}-1\right)=2^3\times \left(2^3-1\right)\end{array}$
On comparing both sides, we get
$\begin{array}{l}{2}^{\mathrm{n}}=2^3\text{ and }{2}^{\mathrm{m}-\mathrm{n}}=2^3\\ \Rightarrow \mathrm{n}=3\text{ and }\mathrm{m}-\mathrm{n}=3\\ \Rightarrow \mathrm{m}=6\text{ and }\mathrm{n}=3\end{array}$
Now, m + n =6+3=9