How can I represent this statement in first order logic?

Question

I'm trying to write the statement below into first order logic:

If someone is a friend of a popstar, then they are a popstar too.

My question is in regards to the quantifiers. Not sure if they are correct:

$$\forall x \, \exists y\, (\,(\, \mathrm{Friend}(x, y)\, \&\, \mathrm{Popstar}(y)\, ) \to \mathrm{Popstar}(x)\,).$$

Answer 1

Considering the statement If someone is a friend of a popstar, then they are a popstar too..

The first order logic for it can be represented as:

$\qquad\forall x\,\big(\exists y\,(\operatorname{Friend}(x, y)\,\&\,\operatorname{Popstar}(y)) \to \operatorname{Popstar}(x)\big)$