Hi,

if $\displaystyle y \in f( \mathbf{A} \cup \mathbf{B}) \Leftrightarrow \exists x \in \mathbf{A} \text{ or } \exists x \in \mathbf{B} \text{ such as }y=f(x)$

$\displaystyle \neg(y \in f( \mathbf{A} \cup \mathbf{B}))= y \not \in f( \mathbf{A} \cup \mathbf{B}))\Leftrightarrow \forall x \not \in \mathbf{A} \text{ and } \forall x \not \in \mathbf{B} \text{ we have }y=f(x)$

it seems right to me but the last part seems weird "we have"...

thanks in advance!