2
$\begingroup$

Let P: "for all natural $n$, exists an integer $p$ such that $n<p<2n$ "


P: $\forall\, n \in \mathbb{N}\, ||\, \exists \, p\in\mathbb {Z} \, ||\, n<p<2n $

¬P: $\exists\, n \in \mathbb{N}\, ||\, \forall \, p\in\mathbb {Z} \, ||\, n>p>2n $

Is correct the translation?

$\endgroup$
2
$\begingroup$

Not quite. The negation of $n<p<2n$ should be $p\le n$ or $p \ge 2n$.

$\endgroup$
  • $\begingroup$ Thank you then ¬P is true right? $\endgroup$ – B. David Oct 12 '17 at 17:01
  • $\begingroup$ With that correction, it will be correct. $\endgroup$ – Alekos Robotis Oct 12 '17 at 17:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.