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

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Ackbach
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Here's this week's problem.

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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.).

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

Here is my answer:

View attachment 3560
 
Attachments
  • Fitch-style natural deduction proof of C ∨ D from premises A ∨ B, A → C and ¬D → ¬B, with each line's justification listed at right.
    First Logic Problem.png
    6.4 KB · Views: 128

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