Getting Nowhere with a Proof Question: Help Needed

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SUMMARY

The discussion centers on the logical equivalence proof of the expression (¬(Q⇒¬P) ∧ ¬((Q∧¬R)⇒¬P )) ⇔ ¬(R ∨ (P ⇒¬Q)). Participants suggest using logical identities such as $\lnot (Q \implies \lnot P) \iff (Q \land P)$ and De Morgan's laws to simplify the expressions. The conversation highlights the importance of understanding proof structures and logical transformations to arrive at the desired equivalence. The participants emphasize clarity in the formulation of the question to facilitate effective assistance.

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  • Understanding of propositional logic and logical equivalences
  • Familiarity with De Morgan's laws
  • Knowledge of implication and negation in logical expressions
  • Ability to manipulate logical formulas and proofs
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Students of mathematics, logic enthusiasts, and anyone involved in formal proof writing or studying logical expressions will benefit from this discussion.

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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