Question

If set A = {1,3,5} , then number of elements in
P{P(A)} is
a) 8
b) 256
c) 248
d) 250​

Answer 1

Answer:

256

Step-by-step explanation:

P(A)=2^3=8

P{P(A)}=P{8}=2^8

256

Answer 2

Answer:

P(P(A)) is the power set of the power set of A

We know that the power set of A contains $2^{n}$ elements

Where n = no of elements in set A

So no of elements in power set of A i.e P(A) = 2³ = 8 elements

Now for the power set of this new set of 8 elements,

The no of elements in the power set of the power set P(P(A)) = 2⁸ = 256

Therefore P(P(A)) contains 256 elements ∴ Option B

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