clarify what are n(A) and P(A) ??

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clarify what are n(A) and P(A) ??

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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 *

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

let P(A) = m

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

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

N[P(A)]=1024=2¹⁰

n [A] =10

n [A] =10