1. Tardigrade
  2. Question
  3. Mathematics
  4. if X is a finite set. Let P(X) denote the set of all subsets of X and let n(X) denote the number of elements in X. If for two finite subsets A, B, n(P(A)) = n(P(B))+15 then n(B) = ........., n(A)=...........

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Q. if X is a finite set. Let $P(X)$ denote the set of all subsets of $X$ and let $n(X)$ denote the number of elements in $X$. If for two finite subsets $A, B, n(P(A)) = n(P(B))+15$ then $n(B) = ........., n(A)=...........$

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Solution:

Let $n\left(A\right) =m, n\left(B\right) =n$
$ n\left[P\left(A\right)\right] =2^{m}.n \left[P\left(B\right)\right] =2^{n}$
$ n\left[P\left(A\right)\right] =n\left[P\left(B\right)\right] +15$
$ \Rightarrow 2^{m} -2^{n} =15 \Rightarrow m =4;n =0$