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2015-10-01T17:19:50+05:30

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A is a set containing some elements.    P(A) = power set = the set of all subsets of A = power set of A.

n(A) = cardinality of A    and    n[ P(A) ] = cardinality of P(A)

if a set A has m elements then P(A) has 2^m elements ...

A = { a, b, c} 
P(A) = {Ф, {a}, {b}, {c}, {a,b}, {b,c}, {c,a}, {a,b,c} }
 n(A)= 3  ,    n [ P(A) ] = 8 = 2³

Thus we can use the combinations and permutations principles to know the cardinality of a power set.
   let  P(A) = m
 then   n[ P(A) ] = 2^m  = 1024 = 2^10
       so  m = n(A) = 10 

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2015-10-05T17:01:55+05:30

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N[P(A)]=1024=2¹⁰
n [A] =10
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