TITLE: Are these two predicate statements equivalent or not?
QUESTION [6 upvotes]: $\exists x \forall y P(x,y) \equiv \forall y \exists x P(x,y)$
I was told they were not, but I don't see how it can be true.

REPLY [2 votes]: Not the same. Compare
(RHS) "Every person has some father or other"
with
(LHS) "There's some guy who fathered every person in the human race"