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Given a knowledge base

$$ P \vee Q, R \implies \neg Q, \neg R $$

I have to prove that $$KB \models P \wedge \neg R$$ is FALSE through model checking..

I derived $$ \neg P \implies Q $$ $$ Q \implies \neg R $$

Can I write $$ \neg P \implies \neg R $$ ? Is this valid? I have absolutely no idea if this statement is right and why...

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  • $\begingroup$ Can you tell us what $KB$ denotes? $\endgroup$ Jan 13, 2016 at 23:52

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Yes, you can conclude that $\neg P\Rightarrow \neg R$. This is because "implies" is a transitive relation. To finish, notice that $P\vee\neg P$ is true in every model (because it's a logical tautology)

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