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Question

If P(A)denotes the power set of Aand A is the void set, then what is the number of elements in P{P{P{P(A)}}}?


A

0

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B

1

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C

4

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D

16

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Solution

The correct option is D

16


Explanation for the correct option.

Step 1: Apply this formula:

If set A has n elements then P(A) has 2n elements.

Since A is void set it means that there is no element in set A.

Hence, the number of elements in the power set of A=20=1.

Step 2: Put the different values of P(A)

When P(A) has 1 element.

P{P(A)}=21=2elements

When P{P(A)} has 2 elements.

P{P{P(A)}}=22=4elements

When P{P{P(A)}} has 4 elements.

P{P{P{P(A)}}}=24=16elements

Hence, option D is correct.


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