hey guys I have this question: Negatate.

$\displaystyle \exists x \forall y (( y=x-7) \vee (x < 2y))$

My answer:

$\displaystyle

\Rightarrow \forall x \exists y \sim(( y=x-7) \vee (x < 2y))$

$\displaystyle \Rightarrow \forall x \exists y ( \sim ( y=x-7) \wedge \sim(x < 2y))$

$\displaystyle \Rightarrow \forall x \exists y ( ( y \neq x-7) \wedge (x \geq 2y))$

This this OK? thanks...