Solving 10-14 Equivalence Arguments: R to neg(w v s)

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SUMMARY

This discussion focuses on solving equivalence arguments involving the logical expressions neg[r ⇒ neg(w ∨ s)] and r ⇒ neg(w ∨ s). The participants analyze the implications of these expressions, particularly in relation to the rules of logical reasoning. Key points include the use of horizontal lines to denote logical deductions and the necessity for clarity in presenting mathematical problems. The discussion emphasizes the importance of formatting and structuring arguments for better comprehension.

PREREQUISITES
  • Understanding of propositional logic and equivalence arguments
  • Familiarity with logical implications and negations
  • Knowledge of logical symbols and their meanings
  • Experience with mathematical typesetting tools for clarity
NEXT STEPS
  • Research the principles of propositional logic and equivalence
  • Learn how to use LaTeX for typesetting mathematical expressions
  • Explore logical deduction techniques and their applications
  • Study common pitfalls in presenting mathematical arguments
USEFUL FOR

Mathematicians, logic students, educators, and anyone involved in formal reasoning or mathematical argumentation will benefit from this discussion.

chelseajjc95
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10.) neg[r\implies neg(w v s)] 13.) r\implies neg(w v s)
----------------------------- R
R^(wvs) --------------------------
neg(w v s)
11.) r\implies neg(w v s)
w v s 14.) r\implies neg(w v s)
------------------------- -------------------------
neg R (w v s)\implies neg r

12.) R
---------------
r v (w v s)
 
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Your post is hard to read. Please do the following to improve it.

  1. Use formula editor to typeset formulas.
  2. The editor does not support alignment in text (unless you use tags such as [m]code[/m] and [m]m[/m]), so you should not rely on it.
  3. Explain the meaning of horizontal lines.
  4. Write the problems in one column. It seems that the text was copied from a two-column PDF.
  5. Write the problem statement in the post body rather than the post title, following https://mathhelpboards.com/rules/.
  6. Show your attempts at solving the problems, or describe the difficulty you are having, following rule 11.
  7. Break the thread into two or three so that each one has one or two problems, foloowing rule 8.
  8. Explain the missing problem 14.
 

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