Another Analysis statement

Here's a new one, all values are assumed to be real:

$\displaystyle (\forall x) (\forall y), (\exists z) \ni xz=y $

To me, this says: For all x and y values, there's some z where x times z equals y.

This is false, but I answered true. The reason why is because if z=1, any x would be equal to any possible y. I thought this meant it was true, but apparently it's not.

Wait, just now I was thinking:

The statement

$\displaystyle (\forall x)(\forall y), x=y$

is false, isn't it? Does this mean that any possible values of x and y have to be equal to each other?