Natural Deduction: Solving Sequents [7/10]

[Mia Fuller]

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

 

[Evgeny.Makarov]

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).

View attachment 6474​

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

   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.