Universal Quantifier: Determining Truth Value in Existential Statements

[mattmns]

I have a question that says, determine the truth value of: $$\exists x \ni \forall y, \exists z \ni xz = y$$

I am thinking this is false because: If you let x = 0, and let y = 1, then there is no value of z that will make the statement true. Am I thinking about this correctly?

 

[StatusX]

Your reasoning would be right if that was a universal quantifier instead of an existential one. All you have to find is one x where this is true and the statement is true.

 

[mattmns]

So if x=1 then for every value of y there is a value of z such that xz = y.

So it is dependent on the statements afterward, the exestential quantifier $$\exists x$$ ? So I would say. There is a value of x such that for any value of y there is a value of z such that xz = y. I guess you are right, it sounds as though it depends on the things that follow. Thanks.