Getting Nowhere with a Proof Question: Help Needed

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Discussion Overview

The discussion revolves around a proof question involving logical equivalences and transformations. Participants are attempting to manipulate the expression (¬(Q⇒¬P) ∧ ¬((Q∧¬R)⇒¬P )) ⇔ ¬(R ∨ (P ⇒¬Q)) to demonstrate its validity or find a solution.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in transforming the given logical expression and feels stuck in their attempts.
  • Another participant suggests using specific logical equivalences, including $\lnot (Q \implies \lnot P) \iff (Q \land P)$ and De Morgan's laws, as potential steps to progress.
  • A different participant questions the clarity of the original question, indicating that the provided formula may need further specification.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the approach to the proof, and multiple viewpoints on how to interpret the question and proceed with the proof remain evident.

Contextual Notes

There may be missing assumptions regarding the proof structure required, and the clarity of the question itself is in dispute, which could affect the discussion's progression.

Leanna
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I'm stuck on this proof question:
(¬(Q⇒¬P) ∧ ¬((Q∧¬R)⇒¬P )) ⇔ ¬(R ∨ (P ⇒¬Q))

I've tried to get rid of the negation and implications but I keep going in circles and I'm getting nowhere near to the equivalence required. I would appreciative if anyone can help me solve this because it's really been doing my head in :/
 
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If you see question marks that's the negation
 
Hi Leanna,

I'm not sure what kind of proof structure is required, but you can obtain the results if you use the following:
$\lnot (Q \implies \lnot P) \iff (Q \land P)$, De Morgan's, and the fact that $Q \land Q \land P \iff Q \land P$.
 
Leanna said:
I'm stuck on this proof question:
(¬(Q⇒¬P) ∧ ¬((Q∧¬R)⇒¬P )) ⇔ ¬(R ∨ (P ⇒¬Q))
What exactly is the question? What you have written is a formula.
 

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