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

In summary, the conversation is about a student needing help with a proof in propositional logic. The given premises are (pv~q)vr and ~pv(q.~p), and the goal is to prove q>r using Copi's 19 Rules, Conditional Proof, and Reductio ad Absurdam. The dot symbolizes AND in the second premise.
  • #1
chanimal
2
0
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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  • #2
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?
 
  • #3
Re: HElP with Propositional Logic!

Assuming only q for conditional proof does not lead us anywhere ??
 
  • #4
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"?
 
  • #5
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.
 

1. What is the purpose of "Prop Logic Proof Help"?

"Prop Logic Proof Help" is a tool used in logic and mathematics to construct and verify logical proofs. It helps to determine the validity of a statement or argument by breaking it down into smaller logical steps, allowing for a clear and organized presentation of the proof.

2. How do you read and interpret the symbols in the statement "pv~q)vr; ~pv(q.~p)/q>r"?

In this statement, the symbol "p" and "q" represent two different propositions or statements. The symbol "v" stands for the logical operator "or", while "~" represents "not". Therefore, the statement can be read as "p or not q, and not p or (q and not p). From these statements, we can conclude that q implies r."

3. What is the meaning of the forward slash symbol ("/") in the statement?

The forward slash symbol ("/") is used to represent the logical operator "therefore" or "implies". In this statement, it indicates that the statements on the left side of the symbol logically lead to the statement on the right side, and thus implies that q leads to r.

4. What is the difference between a valid and an invalid proof?

A valid proof is one in which the conclusion follows logically from the given premises, while an invalid proof is one in which the conclusion does not logically follow from the premises. In other words, a valid proof is a correct and sound argument, while an invalid proof is flawed or incorrect.

5. How can "Prop Logic Proof Help" be used in real-life situations?

"Prop Logic Proof Help" can be used in various fields, including mathematics, computer science, philosophy, and law. It can help to assess the validity of an argument, identify any logical fallacies, and make informed decisions based on accurate reasoning. For example, it can be used in legal proceedings to analyze evidence and determine the strength of a case, or in computer programming to test the logical flow of a code.

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