Here is your post: \(x,y\) aren't empty, infinity series and \(x\cap y=\emptyset\).
Well that is somewhat better but only by a bit.
I presume you are to show that \(\displaystyle P(X\cup Y)\approx P(X)\times P(Y)\) in some sense, saying that the power set of the union is ... what? ... to the Cartesian product of the individual power sets. What does "\(\displaystyle \approx\)" mean to you here? Please define it. I can see a couple kinds of relationship that would apply, but not "approximately equal".
This is a dangerous thing to do: I am going to guess that you are asked to show that