Set Theory and Lists

Question

If A = {b, {b}, ∅} how would we use list notation to write {B: B ⊆ A and B ≠ ∅}

If you could explain what I need to do to solve this that would be much appreciated.

Answer 1

If I understand what you ask correctly you want to list all nonempty subsets of the set A. This is easy if you do the following. Rename the elements of the set A as

1 corresponds to b

2 corresponds to {b}

3 corresponds to the empty set element of A.

Then A={1,2,3}. So the nonempty subsets of A are the sets {1}, {2}, {3}, {1,2}, {1,3}, {2,3} and {1,2,3} and now if you put back the actual elements of the set A instead of 1, 2 and 3 you have your answer.