# Truth Value of Multiple Quantifiers

I have problem determining truth value of statements involving three quantifiers like this one.

$\forall \space x \space \exists \space y$ such that $\forall \space z, \space x+y = z,$ assuming all variables are real numbers.

I normally start these types of problems by trial and error, checking what happens if I fix one variable and vary the other. But since I have three here, I tried picking say x = 4 and z = 3 and see if I can find one y so x+y = z. Is this correct?

If so, is the statement then equivalent to the following? $\forall \space x$ and $\forall \space z, \space \exists \space y$ such that , $\ x+y = z$

I appreciate pointers or ways to tackle this problem. Thanks.

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