Attempt:

(a)Let $\displaystyle I$ be an interpetation, and let $\displaystyle v$ be an I-assignment.

Suppose that $\displaystyle I \models_v A$. We want $\displaystyle I \models_v \exists x A$. And we know that $\displaystyle I \models_v \exists x A$ iff there is some $\displaystyle d \in D$ with $\displaystyle I \models_{v \frac{d}{x}}A$. But how do we show that we have such a d?

(b)Suppose $\displaystyle I \models_v \exists x Ax$, I have to show that $\displaystyle I \not{\models_v} Ax$. But I'm confused because assuming $\displaystyle I \models_v \exists x Ax$ means there is some d in the domain with $\displaystyle I \models_{v \frac{d}{x}} Ax$. What could I do? Are there better ways to show that the implication doesn't hold?