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?
Well that is better. But still this is confused: {x} is an element of S and {x} is not included in S.
Does that mean BUT
Let be the set of integers and be the powerset of ( set of all subsets).
If then it has the property that .
Please do not edit a post to clarify. Post a new reply please.
" \{x\}\in S BUT \{x\}\not\subset S~" that is what I am trying to understand, however I do not understand anything that you have provided underneath.
I am sorry for taking your time. Can you please close this thread.