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I have a quick question. How can I simplify

$\neg(\neg P \lor (\neg Q \land \neg R))$ to $P \lor \neg(\neg Q \land \neg R))$

in natural deduction for propositional logic, and is this even allowed? What kinds of proofs would I have to use?

Thanks in advance.

Frank Hubeny
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user8679576
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1 Answers1

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Here is a proof in a Fitch-style proof checker to show how one can start with $\neg(\neg P \lor (\neg Q \land \neg R))$ as a premise and derive $P \land (Q \lor R)$. This will show how to approach applying not across sentences within brackets or parentheses. Also this may be what the OP intended to derive.

enter image description here

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

Frank Hubeny
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