MHB Prop Logic Proof Help: (pv~q)vr; ~pv(q.~p)/q>r

[chanimal]

i need help with a proof:
(pv~q)vr
~pv(q.~p) / q>r

this is some propositional logic
thanks all

 

[Ackbach]

Re: HElP with Propositional Logic!

i need help with a proof:
(pv~q)vr
~pv(q.~p) / q>r

this is some propositional logic
thanks all

So, using $\LaTeX$ to typeset it nicely (you can right-click to see what code I used), we have that you need to prove

$(p\;\lor\sim\!q) \lor\, r$

$\sim\! p \, \lor (q \; \cdot \sim\! p) \qquad / \therefore \; q\supset r$

A quick shorter truth table analysis shows this to be a valid argument. So, we need to prove a horseshoe. The Conditional Proof allows us to prove a horseshoe. So, what would you assume?

 

[solakis1]

Re: HElP with Propositional Logic!

Assuming only q for conditional proof does not lead us anywhere ??

 

[Evgeny.Makarov]

Re: HElP with Propositional Logic!

i need help with a proof

If you need a derivation in some formal system, please specify which system. See https://driven2services.com/staging/mh/index.php?threads/29/. Otherwise please describe what type of proof you need.

Also, is there any significance of a period in ".~p"?

 

[Ackbach]

Re: HElP with Propositional Logic!

If you need a derivation in some formal system, please specify which system. See https://driven2services.com/staging/mh/index.php?threads/29/. Otherwise please describe what type of proof you need.

Also, is there any significance of a period in ".~p"?

This is one of my students. It's Copi's 19 Rules, plus Conditional Proof and Reductio ad Absurdam thrown in for good measure. The dot means AND.