Can there exists three sets: $A \subset B$, $B \in C$, $A \in C$ Can there exists three sets: $A \subset B$, $B \in C$, $A \in C$, if not, why not?, if yes, give an example.
My example:
A={$a,b$}
B={$a,b,c$}
C={{$a,b$},{$a,b,c$}}
Is this all? It seems this is a tricky question and there's something I'm missing. Thank you for your help!
Edit: fix typo
 A: If A if a subset of B and 
If B is an element or subset of C 
Then A can only be a subset/element of C. 
Thanks for clarifying. i misinterpreted the relationship b/w B and C. 
A: Written down in plain text, your question reduces to the existence of two sets, one of which a proper subset of the other such that they are both elements of a third set! There are infinitely many instances of triplets of sets satisfying such a configuration: for any set $A$ there must exist an object $a$ not an element of it (otherwise $A$ would become a universal set with respect to the relation of set-theoretical membership, situation which is prohibited by the axioms of almost any modern axiomatic system for formal mathematics); therefore, by setting $B=A \cup \{a\}$ you automatically have $A \subset B$; furthermore, by considering $C=\{A, B\}$ you will have obtained a triplet of sets as specified starting from any given set.
A: My example given above is correct, therefore
$$\exists A,B,C \hookrightarrow A \subset B, A \in C, B \in C $$
