Question

If A={1}, then find the no. of elements in P[P[P(A)]].

Answer 1

P(A)?

Answer 2

my book has the same question as i've posted.

Answer 3

i cant remember what was P(A) :(

Answer 4

P(A) = { {}, {1} }

Answer 5

P[P(A)] = { {}, {{}}, {{1}}, { {}, {1} } }

Answer 6

P[P(A)] has 4 elements. Next level of power set would have 2^4 elements

Answer 7

is the no. of elements = 2 ?

Answer 8

2^4 = 16

Answer 9

in those 16 are - {} {1} and all other are in pair with {}.

Answer 10

so it will have {} {1} {1}{1}{1}{1}{1}{1}{1}{1}{1}..16times

Answer 11

We can list them but gets messy
instead we use the formula

Let S be a finite set with N elements. Then the powerset of S (that is the set of all subsets of S ) contains 2^N elements.

Answer 12

it contains 16 elements
{}
{{}}
{{{}}}
{{{1}}}
{{ {}, {1} }}
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{ {}, {{}}, {{1}}, { {}, {1} } }