What is ({({(∅)})}) explicit written?

Question

I am not sure what ({({(∅)})}) is. I could say what (((∅))) but it does not help me much.

Thanks in adavance.

Answer 1

HINT

The difference between ({({(∅)})}) and (((∅))) is that the former takes the power set of the set {({(∅)})}. And the set {({(∅)})} is a singleton set: a set with exactly one element, that being ({(∅)})

Likewise, ({(∅)}) itself is the powerset of the set {(∅)}, which is the singleton set containing the one element (∅)

Finally the powerset of a singleton set is the set containing two elements: that set itself, and the empty set, since those are the only two subsets of the singleton set.

As such, ({(∅)}) = {{(∅)}, ∅}.

And, since I assume you need if you need to write out the (∅) (which is {∅}), you get:

({(∅)}) = {{{∅}}, ∅}

Can you take it from here?