If n[P(A)] = 1024 find n(A)
kvnmurty:
clarify what are n(A) and P(A) ??
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Answered by
49
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
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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Answered by
46
n[P(A)]=1024=2¹⁰
n [A] =10
n [A] =10
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