Suppose We have a set called ${A}$ and we let it equal to $A = \{a \in \mathbb{Z} \mid a^2 = 3\}$ and we let ${P(x)}$ be the predicate ${x \in \mathbb{Z} }$
Problems:
1.) ${\forall x \in A }, P(x)$
2.) ${\exists x \in A }, P(x)$
Reasoning:
For both of these problems, The first problem that I see is that equation ${a^2 = 3}$ will never be true for number in the integer set and and since ${a}$ is an integer, it has a blank set.
Thus I reason both can't hold.
You have good progress. Certainly $A = \emptyset$, so that's good. So statements of the form $\forall x \in \emptyset\, P(x)$ are always true vacuously. On the other hand, statements of the form $\exists x \in \emptyset\, P(x)$ are always false, as they require finding an element of the empty set.