Sorry for the dumb question, but I still have to get familiarity with this notions.
I have two sets $x$ and $y$ s.t. $x,y\in WF$, I proved that also $\{x\},\{x,y\}\in WF$.
Now I am asked to calculate the rank of $\{x\}$ and of $\{x,y\}$ in terms of $rk(x)$ and of $rk(y)$. This was my thought process:
Using the rank formula I get $rk(\{x\}) = \sup\{rk(z)+1 :z\in\{x\}\} = \sup\{rk(x)+1\} = rk(x)$. But this doesn't seem to be correct since $x\in\{x\} \implies rk(x)<rk(\{x\})$. Same reasoning for $rk(\{x,y\}$) and I get $rk(\{x,y\}) = \max\{rk(x),rk(y)\}$.
Where am I wrong?