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Can we use double negation and distribute it like this

$$(\neg \neg p \lor -q ) \equiv \neg(\neg p \lor q)$$

But De Morgan's law isn't like what I did above!

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  • $\begingroup$ $ \neg $ \neg $\endgroup$ – Kenny Lau Sep 5 '17 at 16:19
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Can we use double negation and distribute it like this

$$(\neg \neg p \lor -q ) \equiv \neg(\neg p \lor q)$$

No, you can't. Here is why:

When $p$ and $q$ are true, then $\neg \neg p \lor q$ is true, but $\neg(\neg p \lor q)$ is false. So these are not equivalent.

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  • $\begingroup$ You're right; I've deleted my answer. $\endgroup$ – Theoretical Economist Sep 5 '17 at 16:49
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    $\begingroup$ @TheoreticalEconomist I almost added that comment to my Post, as I figured several people would do just what you did :) $\endgroup$ – Bram28 Sep 5 '17 at 16:51
  • $\begingroup$ I was wondering why you hadn't pointed that out. It turns out that you just read the OP more carefully than I did. :) $\endgroup$ – Theoretical Economist Sep 5 '17 at 16:52
  • $\begingroup$ I wasn't aware that we should evaluate () before the negation.Thanks! $\endgroup$ – Sun292 Sep 5 '17 at 16:54
  • $\begingroup$ @Sun292 Yes, it's just like other mathematical expressions. Glad I could help! $\endgroup$ – Bram28 Sep 5 '17 at 16:56

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