Can you prove $C\lor D$ using given premises?

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SUMMARY

The discussion centers on proving the statement $C \lor D$ using the premises $A \lor B$, $A \to C$, and $\neg D \to \neg B$. Participants are encouraged to utilize any valid first-order deduction system, with specific mention of Copi's 19 Rules and Natural Deduction. The problem remains unsolved in the forum, indicating a challenge for users familiar with logical deduction techniques.

PREREQUISITES
  • Understanding of first-order logic
  • Familiarity with Copi's 19 Rules
  • Knowledge of Natural Deduction methods
  • Ability to manipulate logical statements and implications
NEXT STEPS
  • Study the principles of first-order logic deduction
  • Review Copi's 19 Rules for logical proofs
  • Practice Natural Deduction with various logical statements
  • Explore common strategies for proving disjunctions in logic
USEFUL FOR

This discussion is beneficial for students of logic, educators teaching logical reasoning, and anyone interested in mastering proof techniques in first-order logic.

Ackbach
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Here's this week's problem.

-----

From $A\lor B, \; A \to C, \; \neg D \to \neg B$, prove
$C\lor D$. You may use any valid first-order deduction system, but you
must indicate which one you are using (Copi's 19 Rules, Natural
Deduction, etc.).

-----

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 Undergraduate POTW; I was hoping this problem could at least tempt Evgeny! ;)

Here is my answer:

View attachment 3560
 

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