Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.


$P \Leftrightarrow (\exists x: A)$ be stated alternatively as

$\overline{P} \Leftrightarrow \neg (\exists x: A)$


$\overline{P} \Leftrightarrow (\forall x: \neg A)$ ?

share|cite|improve this question
What do you mean by $::$? I haven't seen that notation before. – Alexander Gruber Oct 5 '12 at 4:04
@AlexanderGruber: Removed it, it wasn't relevant to the question! – TCSGrad Oct 5 '12 at 4:13

1 Answer 1

up vote 4 down vote accepted

$P \Leftrightarrow Q$ is the same as $P \Rightarrow Q$ and $Q \Rightarrow P$
Those may be converted as $\neg Q \Rightarrow \neg P$ and $ \neg P \Rightarrow \neg Q$
Which is then indeed what you are asking about: $\neg P \Leftrightarrow \neg Q$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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