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A is a set containing some elements.

P(A) = set of all subsets of A = power set of A.

n(A) = cardinality of A

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

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

so n[ P(A) ] = 2^m = 1024 = 2^10

so n(A) = 10

P(A) = set of all subsets of A = power set of A.

n(A) = cardinality of A

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

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

so n[ P(A) ] = 2^m = 1024 = 2^10

so n(A) = 10