Power set of a set containing a set I need some help understanding this concept a little better. I understand the general power sets, but only worked nice and easy examples where only the set consisted of only single elements like $\{a,b,c\}$. I can do that power set, but I am confused on the power set of a set containing a set. The problem I am trying to work is $\{a,\{a,b\}\}$. Typically when you have a set $\{x,y\}$ the power set is $\{\{x\},\{y\},\{x,y\}\}$ so would this problem be similar to that where $\{y\}=\{a,b\}$? Or would I then need to perform a second power set on the inner set?

Let $X=\{a,\{a,b\}\}$. The set $X$ has two elements: nothing more, nothing less. Then,
$$\mathcal P(X)=\big\{\emptyset,\{a\}, \{\{a,b\}\}, \{a,\{a,b\}\}\big\}$$
If things don't become clear, you can try "encapsulating" the element $\{a,b\}$ calling it $c$, so you can now write $X=\{a,c\}$.
