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How would I write a denial of the following proposition.

Neither $z<s$ nor $z\le t$ is true. (Assume z,t and s are natural numbers)

I think $P=z<s$ is not true

$Q=z\le t$ is not true

And neither can be seen as both so that would and I think.

$\neg (P\wedge Q)$

So then would be $\neg P \vee \neg Q$

As the denials?

Fernando Martinez
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  • The word you're looking for is "negation", not "denials". Denial means that I'm not allowing you to do something, negation means the opposite [truth value] of what that was said. – Asaf Karagila Jun 10 '14 at 16:23
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    Hmm I guess negation would seem more correct I use denial because of the text book question says "denial" – Fernando Martinez Jun 10 '14 at 16:26

1 Answers1

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That is fine, but you might want to translate back:

$\lnot P \lor \lnot Q$ means not ($\underbrace{\lnot (z\lt s)}_P)$), or not $(\underbrace{\lnot (z\leq t)}_Q)$, in other words, $z \lt s$ or $z \leq t$

amWhy
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