Does the order of the quantifiers matter?

1.3

--- No, if we have several consecutive quantifiers of the same type:

?x?yQ(x,y) ? ?y?xQ(x,y) ?x?yQ(x,y) ? ?y?xQ(x,y)

--- Yes, if we have different quantifiers:

?x?yQ(x,y) ? ?y?xQ(x,y)

Counterexample: Let Q(x,y) mean “x+y=0”, and let the universe of

discourse be the set of all real numbers. What is the truth value of:

?x?yQ(x,y) ?

--- true

?y?xQ(x,y) ?

--- false

Previous slide

Next slide

Back to first slide

View graphic version