What Are the Elements of P(P(∅))?

[Bashyboy]

Homework Statement

P(P(∅))

Homework Equations

The Attempt at a Solution

I did the inner power set first: {{∅}, ∅}
Then I took the power set of that: {{{∅}}, {∅}, {{∅}, ∅}, ∅}
But according to the answer, there is only two elements.

 

[stephenkeiths]

That first power set doesn't look quite right to me.

is {∅} an element of ∅??

What are all the elements of ∅?

What are all the subsets of ∅?