How Can a Set Both Belong to and Be a Subset of P(N)?

NecroWinter
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Hi there, here's the question I am given, i will provide the answer that I think is correct, do you mind checking it and possibly pointing out where I am wrong if I am?

Give an example of a set S such that:
a) S is a subset P(N)
b) S belongs to P(N)
c) S belongs to P(N) and |S|=5

here are my answers:

a) {1,2,3}
b) {{1}}
c) {1,2,3,4,5}
 
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Hey NecroWinter and welcome to the forums.

Just to clarify what is the set P(N)? Is this just all the natural numbers or the power set of the entire set of natural numbers?
 
You have the answers for A and B switched.
 

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