Problem of the Week # 163 - May 12, 2015

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SUMMARY

The discussion centers on constructing a formal proof for the propositional statement $(P\to (Q\to R)) \leftrightarrow ((P\land Q)\to R)$ using a specified deductive system. Participants are encouraged to utilize Copi's 19 Rules or Natural Deduction for their proofs. The problem remains unanswered, highlighting the need for engagement in formal logic discussions. The lack of responses indicates a gap in understanding or interest in this specific topic.

PREREQUISITES
  • Understanding of propositional logic and its symbols, including implications ($\to$), conjunctions ($\land$), and biconditionals ($\leftrightarrow$).
  • Familiarity with formal proof techniques, specifically Copi's 19 Rules or Natural Deduction.
  • Basic knowledge of logical equivalences and how to manipulate logical statements.
  • Experience with mathematical reasoning and proof construction.
NEXT STEPS
  • Study Copi's 19 Rules for formal proofs in propositional logic.
  • Learn Natural Deduction techniques for constructing logical arguments.
  • Explore logical equivalences and their applications in formal proofs.
  • Practice constructing formal proofs with various propositional statements to enhance understanding.
USEFUL FOR

Students of mathematics, logic enthusiasts, and educators seeking to deepen their understanding of formal proofs in propositional logic.

Ackbach
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Here is this week's POTW:

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Construct a formal proof of the following propositional statement: $(P\to (Q\to R)) \leftrightarrow ((P\land Q)\to R)$. Here $\to$ means "implies", $\leftrightarrow$ means "if and only if", and $\land$ means "and". Make sure to mention what deductive system you are using (Copi's 19 Rules, Natural Deduction, etc.).

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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
 
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No one answered this week's POTW. Here is my solution:

This is a Fitch-style proof using natural deduction.

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