Thu, Oct 01, 2009 -- quantifier order
Posted by: A. Patrice Seyed

To review, the order of the quantifiers does matter when the quantifiers
are different. (Take A to be a universal quantifier and E to be an
existential quantifer in the following.)

where L(x,y) represent "x loves y", and x and y are the domain of all
people:

AxEy L(x,y)

represents that, for all people, there is some person that they love (not
necessarily the same person)

but

EyAx L(x,y)

represents that there exists some person that all people love (this
"some person" is the same person).


See
http://www.cse.buffalo.edu/~rapaport/191/S09/transtip-pnllogic.html
#53, 3, for further details.