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.

Nikolaos P.

10/22/20

Mazzy A.

Great, thanks!10/22/20

Mazzy A.

Thanks! I think the part that was confusing me was the usage of ‘B: B ⊆ A‘ because the letter b was also used in the elements. Is it irrelevant what letter is used in the second part? I.e. in ‘B: B ⊆ A’ the B is just used as a place holder, it could have easily been X, etc. Does it mean everything that is in B is also in A, which is why you listed all the subsets of A?10/22/20