Question

Subject: Maths
Lesson: Set language
Question :
If n[P(A)]=1024,find n(A)
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Answer 1

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 cardinality of P(A)

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

A = {a,b,c}

P(A) = {D, {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