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

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Discussion Overview

The discussion revolves around a proof in propositional logic involving the expressions (pv~q)vr and ~pv(q.~p) leading to the conclusion q>r. Participants seek assistance in deriving this proof, exploring various methods and interpretations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the proof using LaTeX and suggests that a truth table analysis indicates the argument is valid.
  • Another participant questions the effectiveness of assuming only q for the conditional proof, indicating it does not lead to a useful outcome.
  • A request for clarification on the formal system required for the proof is made, along with a question about the significance of a period in ".~p".
  • A later reply clarifies that the dot represents AND and references specific rules from a formal system, indicating a connection to educational material.

Areas of Agreement / Disagreement

Participants express differing views on the approach to the proof, with some suggesting methods like truth tables and conditional proofs, while others indicate uncertainty about the assumptions and formal systems involved. No consensus is reached on the best method to proceed.

Contextual Notes

There are limitations regarding the clarity of the formal system needed for the proof and the interpretation of symbols used in the expressions, which remain unresolved.

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

this is some propositional logic
thanks all
 
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Re: HElP with Propositional Logic!

chanimal said:
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?
 
Re: HElP with Propositional Logic!

Assuming only q for conditional proof does not lead us anywhere ??
 
Re: HElP with Propositional Logic!

chanimal said:
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"?
 
Re: HElP with Propositional Logic!

Evgeny.Makarov said:
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.
 

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