MHB Natural Deduction: Solving Sequents [7/10]

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The discussion focuses on completing natural deduction proofs for specific sequents involving logical operators and implications. Participants emphasize the importance of accurately describing inference rules and suggest using Fitch-style calculus for clarity. One user provides a sample derivation to illustrate the process, indicating that a contradiction can be used to derive negations. There is also an invitation for the original poster to share their attempts at the second derivation for further discussion. Overall, the conversation aims to assist in achieving the required line counts for the proofs.
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Hi guys, does anyone know how to complete proofs of natural deduction for these sequents? ¬ (P ˅ Q), R → P : ¬ R [7]

(P & Q) → ¬ R, : R → (P → ¬ Q) [10]the {7} in brackets indicates how many lines each answer should be. I attempted both but my amount of lines were not 7 or 10

Would really appreciate any help. Thank you
 
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If we are talking about the number of lines, then we should describe the inference rule more precisely. After all, the following derivation is also natural deduction (in tree form).


I assume you are using the so called Fitch-style calculus. Then you can have something like the following.

Code:
   R
   R -> P
   P
   P \/ Q
   ~(P \/ Q)
   _|_
~R

By $$\bot$$ I denote contradiction. You may have a different rule for deriving negations.

You could post your attempt at the second derivation, and we can discuss it.
 

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