Q. 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

Sets Report Error

A

9

23%

B

13

16%

C

8

48%

D

10

13%

Solution:

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

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Q. 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

9

13

8

10

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