Sorry if this is a really dumb question, but...
After reading How to Prove it, I've become a little confused. On page 70, an example stating something similar to this is provided:
$[\exists x P(x) \land \exists x Q(x)]$ and $\exists x [P(x) \land Q(x)]$ are two different things,
and says that for the first statement, there could be a person that makes p(x) true, and there could be a different person that makes q(x) true.
I thought that if we picked an x value, it would apply across the whole statement? What is the purpose of using different variable names if not?
Thanks in advance!