I am struggling a bit with giving the useful negation and the written statement:
For (b) below:
(i) Assign a universal set to each variable, label each component statement with a symbol;
(ii) write a useful negation of the statement symbolically; and
(iii) Give a useful written negation of the statement.
(b) For every positive real number y there exist real numbers x and z such that $y = x^2 − 1$ and $y = e^z$.
Here is my answer:
(i) $U$x = $R$, $U$y = $R^+$, $U$z = $R$,
$R(x,y)$: $y = x^2 -1$,
$S(x,y)$: $y = e^z$
(iii) There is a positive real number $y$ such that for all real numbers $x$, $y$, $y$ $\neq$ $x^2-1$ or $y$ $\neq$ $e^z$
I am not quite sure on the negation though.