I have been working on this problem for hours and cant seem to understand how to go about doing it. The question is to prove that
Is not equivalent to
by giving an interpretation which is a model for one, but not for the other.
I don't see how simply switching the position of the existential quantifier makes a difference. Can someone please give me some pointers? Thank you.
Hint: Let $g(w,x,y,z)$ hold if $x\lt y$, domain the reals.