Show that there is no set satisfying the following properties.

(a) If $X\in A$, then $\mathcal P(X)\in A$

(b) If $T\subseteq A$, then $\bigcup T\in A$

I wonder how to prove this problem.

According to the [note](http://karagila.org/files/set-theory-2017.pdf) that I saw this problem, this problem is called Hilbert's Paradox. But when I searched for Hilbert's paradox, I could only find something about the infinite-hotel. Is it related to this problem?