Sets, Relations & Functions Question - None

Question

The total possible subsets of sets A and B are $2^m$ and $2^n$ respectively. If $2^m - 2^n = 56$ and $2^{m-n} = \frac{3}{2}$, find $m + n$.

Accepted Answer

Solution:

Given: $2^m - 2^n = 56$ and $2^{m-n} = \frac{3}{2}$

From the first equation: $2^n(2^{m-n} - 1) = 56$

On comparing: $2^n = 2^3$ and $2^{m-n} = 2^3$

Therefore: $n = 3$ and $m - n = 3$

Thus: $m = 6$ and $n = 3$

Therefore: $m + n = 6 + 3 = 9$

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