# Logic assigment: prove (A->C) v (A->D) therefore A->CvD

just started logic, and I cannot seem to know know to solve this assigment. 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)\$ – Hassan Jolany Sep 21 at 10:08
• The fist step is to apply Disjunction-elim to the premise and then the two sub-proofs assuming A. – Mauro ALLEGRANZA Sep 21 at 10:26
• @HassanJolany - there is no math formula processor on PhilSE. – Mauro ALLEGRANZA Sep 21 at 10:54
• I'll look at your suggestions. Thank you both. – SimpleOne Sep 21 at 20:09

## 1 Answer

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:

• 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 at 21:22