Help needed! Propositional Logic and Rules of Inference question, Discrete Structures. | Mathematics | Page 1

molten harbor Sep 17, 2023, 7:25 PM

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Question is Prove the conclusion. I attached my own working and the 5 statements + conclusion is the question.
Are the bolded parts (6, 7) legal moves? I have a feeling its wrong and I just want it to be simpler than it is. If I am wrong, feel free to explain why cause I've been stuck for a while.

oak cloudBOT Sep 17, 2023, 7:25 PM

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molten harbor Question is Prove the conclusion. I attached my own working and the 5 statements...

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dire matrix Sep 17, 2023, 8:31 PM

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No that's legal. $J \land C$ is more restrictive than $J$. That means if you prove for $J$, you prove for $J \land C$.

mystic shaleBOT Sep 17, 2023, 8:32 PM

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Yojda

dire matrix Sep 17, 2023, 8:34 PM

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In a more formal way, $(J \land C) \Rightarrow JKS$ \
$\equiv \neg J \lor \neg C \lor JKS$ \
And \
$J \Rightarrow JKS$ \
$\equiv \neg J \lor JKS$

mystic shaleBOT Sep 17, 2023, 8:35 PM

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Yojda

dire matrix Sep 17, 2023, 8:38 PM

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And you have $\neg J \lor JKS \Rightarrow \neg J \lor \neg C \lor JKS$

mystic shaleBOT Sep 17, 2023, 8:38 PM

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Yojda

molten harbor Sep 17, 2023, 8:45 PM

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dire matrix And you have $\neg J \lor JKS \Rightarrow \neg J \lor \neg C \lor JKS$

That makes so much more sense now. Thanks!

austere walrusBOT Sep 17, 2023, 8:45 PM

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@molten harbor has given 1 rep to @dire matrix

#Help needed! Propositional Logic and Rules of Inference question, Discrete Structures.