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.