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  4. If the difference between the number of subsets of two sets A and B is 120 , then n(A × B) is equal to

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Q. If the difference between the number of subsets of two sets $A$ and $B$ is $120$ , then $n\left(A \times B\right)$ is equal to

NTA AbhyasNTA Abhyas 2020

Solution:

Let, $n\left(A\right)=\alpha \&n\left(B\right)=\beta $
Given, $\left|2^{\alpha } - 2^{\beta }\right|=120\Rightarrow \left(\alpha , \beta \right)\equiv \left(7,3\right),\left(3,7\right)$
$\therefore n\left(\right.A\times B\left.\right)=7\times 3=21$