Let A and B be two finite sets with m and n e | vedclass

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(A) Given that the number of subsets of set $A$ is $2^m$ and the number of subsets of set $B$ is $2^n$.According to the problem,$2^m - 2^n = 56$.$2^n(

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$10$

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(A) Given that the number of subsets of set $A$ is $2^m$ and the number of subsets of set $B$ is $2^n$.According to the problem,$2^m - 2^n = 56$.$2^n(2^{m-n} - 1) = 56 = 8 	imes 7 = 2^3 	imes 7$.Comparing the powers of $2$,we get $2^n = 2^3$,which implies $n = 3$.Also,$2^{m-n} - 1 = 7$,so $2^{m-n} = 8 = 2^3$.Thus,$m - n = 3$,and substituting $n = 3$,we get $m = 6$.The points are $P(6, 3)$ and $Q(-2, -3)$.The distance $PQ = \sqrt{(6 - (-2))^2 + (3 - (-3))^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$.Therefore,the correct option is $A$.

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of set $A$ is $56$ more than the total number of subsets of set $B$. Then the distance of the point $P(m, n)$ from the point $Q(-2, -3)$ is

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