Prove P ∨ Q, Q ∨ R, P → ¬R |- Q with natural deduction.

  1. P ∨ Q, premiss
  2. Q ∨ R, premiss
  3. P → ¬R, premiss ... ... Conclusion, Q

I dont know how to properly solve this question?

I know somewhat how to solve similar questions like below, but on this specific question above I dont know where to start.

  • 1
    $\begingroup$ This should be asked on Mathematics, not here. $\endgroup$
    – user16034
    Sep 25, 2023 at 11:38
  • $\begingroup$ The idea is to do OR-elimination. The intuition behind OR-elimination is that you're going to do a case analysis. If you choose to eliminate $p \lor q$, you will first consider the possibility that $p$ is true, and then consider the possibility that $q$ is true. The meaning of the rule is that regardless of whether $p$ or $q$ is true, you must reach the same conclusion either way. That's the idea of OR-elimination. So that's your first step. And that's what you see in the proof in lines 3 and 5. Reply if you have other questions. $\endgroup$
    – ShyPerson
    Sep 29, 2023 at 1:55


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