just started logic, and I cannot seem to know know to solve this assigment. I've tried this:

I've tried this

I suspect I cannot break the disjunction on P, only with A hypotesis. How should I split it?

Thank you

  • $A\implies C $ is equivalent with $\neg A\ lor C$ so we get $(\neg A\lor C ) \lor (\neg A\lor D)$ hence $\neg A \lor (C\lor D)$ so $A\implies (C\lor D)$ – user47436 Sep 21 '20 at 10:08
  • 2
    The fist step is to apply Disjunction-elim to the premise and then the two sub-proofs assuming A. – Mauro ALLEGRANZA Sep 21 '20 at 10:26
  • @HassanJolany - there is no math formula processor on PhilSE. – Mauro ALLEGRANZA Sep 21 '20 at 10:54
  • I'll look at your suggestions. Thank you both. – SimpleOne Sep 21 '20 at 20:09

You need to resolve each of the cases into the term you want to proof to be able to use a disjunction elimination, like so: enter image description here

  • I also tried to solve the subproof A->C, etc. but it didn't occur to me to nest another subproof for that. Now it looks so simple. Thanks for the complete answer. I know the socratic method is usually best to get a good understanding, but in my case I needed this step-by-step guide. – SimpleOne Sep 26 '20 at 21:22

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