As requested:

What I am asking, can {x} ∈ S and {x} ⊊ S, where x is a integer value and S is the set?

The problem is:

Find a pair set S such that {x} is an element of S and {x} is not included in S.

My answer is, that this is not possible.

From what I know:

It is possible to have a set, A, and second set, B. Set B can be contained as an element of set A, however that also means that any element contained in set B is included in A. So A={B} while B={0, 3}, then A = {{0,3}}.

Is my logic correct?

--- Original

Sorry, but I am a mature student taking this course Discrete Structures for the first time and am having a hard time trying to understand a particular situation dealing with sets.

What I am feeling that I should know, to answer a particular question, is if a element can be apart of a set but not included within it. I clearly do not understand my notes, practice and reading.

Can someone explain to me if this situation is possible or not?