The finite sets $A$ and $B$ have $m$ and $n$ elements respectively. if the total number of subsets of $A$ is 112 more than the total number of subsets of $B$, then the volume of $m$ is

Question

Dr. Abubacker · Accepted Answer

(a)
According to the given condition,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2^{m} = 112 + 2^{n}$
$\Rightarrow \ \ \ \ \ 2^{m} - 2^{n} = 112$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ m = 7,\ n = 4$

Q. The finite sets $A$ and $B$ have $m$ and $n$ elements respectively. if the total number of subsets of $A$ is 112 more than the total number of subsets of $B$, then the volume of $m$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?