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 $A$ is a subset of $D$, since every element of $A$ lies in $D$. The converse also holds, so you have $A = D$ in this case, but $A$ is not an element of $D$. 
In the second case, $A$ is an element of $D$. For the last case, $A$ is again an element , but not a subset.
