Elements and Subsets This is my first discrete math course so this questions might seem simple but I would like clarification.
Say I have a set $A=\{1,2,3\}$ and a set $D=\{1,2,3\}$. Is it true that set $A$ is both an element and a subset of set $D$?
Now say $D=\{\{1,2,3\}\}$. Is it true that set $A$ is no longer an element of $D$ because $D$ is a set which contains a set that contains $1,2,3$?
A third case. Say I have set $D=\{x,16,\{1,2,3\}\}$. Is set $A$ an element and proper subset of $D$? 

In the first case, $A = D$, which is different from $A \subseteq D$ (true) or $A \in D$ (false). In the second case, $A \in D$, while $A \ne D$ and $A \not\subseteq D$.  
