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Probability Level 3

If $A = \phi$ , then number of elements in $P(P(P(P(P(A)))))$ is

Details :

$A = \phi$ means set A has no element.
P(A) denotes the power set of A

2^1

2^{16}

2^0

2^4

2^2

2^{32}

2^8

1 solution

Akhil Bansal
Sep 24, 2015

$\Rightarrow A = \phi$

$\Rightarrow n(A) = 0 \quad \quad \quad[ \text{n(A) denotes number of elements in A ] }$

$\Rightarrow n(P(A)) = 2^n = 2^0 = 1$

$\Rightarrow n(P(P(A))) = 2^1 = 2$

$\Rightarrow n(P(P(P(A)))) = 2^2 = 4$

$\Rightarrow n(P(P(P(P(A))))) = 2^4 = 16$

$\Rightarrow n(P(P(P(P(P(A)))))) = \boxed{2^{16}}$

Bhaiya, edit from your 3rd implication onwards. For example, in 3rd implication, I think you meant n(P(A)) = 1, because P(A) = 1 when A is empty makes no sense. Include cardinality function every time you are calculating the number of elements in power set, not the power set itself.

Venkata Karthik Bandaru - 5 years, 8 months ago

Thanks! Edited

Akhil Bansal - 5 years, 8 months ago

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