Let P(X) denote power set of a set X. If A is the null set, then the number of elements in P(P(P(P(A)))) is _________.
Explanation:
P(A) is the power set of A.
Number of elements in power set of A = 2n where n is the number of elements in A.
Since A is a null set, number of elements in P(A) = 20 = 1.
Power set of P(A) i.e., P(P(A)) will have 21 = 2 elements.
Power set of P(P(A)) i.e., P(P(P(A))) will have 22 = 4 elements.
Power set of P(P(P(A))) i.e., P(P(P(P(A)))) will have 24 = 16 elements.
Hence, 16.
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