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Question

If A=,P(A) denotes power set of A, then number of elements in p(p(p(p(pA))))) is

A
1
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B
24
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C
25
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D
216
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Solution

The correct option is C (24)


As we know that the number of elements in a power set P(X) is 2n
Where n is the number of elements in set X.
Given number of elements in A is 0 as A is empty set.
So, number of elements in power set P(A) is n(A)=20=1 [since, n=0]
Similar way, n[P{P(A)}]=21=2
n(P(P{P(A)}))=22=4
P{P{P{P(A)}}}=24
Hence, option B is correct


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