TITLE: What's the difference between $∀x\,∃y\,L(x, y)$ and $∃y\,∀x\,L(x, y)$?
QUESTION [21 upvotes]: Everybody loves somebody. $∀x\,∃y\,L(x, y)$
There is somebody whom everybody loves. $∃y\,∀x\,L(x, y)$

What's the difference between these two sentences? If they are same, can I switch $\exists y$ and $\forall x$?

REPLY [13 votes]: I'm late to the party but:  replace "loves somebody" with "has someone as a mother".
Everbody has a mother.
vs.
There is somebody who is everybody's mother.
?????