Can anyone solve this using Natural Deduction rules? (ND)

I have attached a file showing the same problem with better symbols.

I ^ ~(TvD) -> R given

D^N -> V given

I -> ~T given

N^~V -> R goal

Thank you !!!(Wink)

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- Jan 11th 2010, 10:58 AMSavvasclHelp with Logic (Natural Deduction)
Can anyone solve this using Natural Deduction rules? (ND)

I have attached a file showing the same problem with better symbols.

I ^ ~(TvD) -> R given

D^N -> V given

I -> ~T given

N^~V -> R goal

Thank you !!!(Wink) - Jan 11th 2010, 01:57 PMemakarovQuote:

I ^ ~(TvD) -> R given

D^N -> V given

I -> ~T given

N^~V -> R goal

(I /\ ~(T \/ D)) -> R given

(D /\ N) -> V given

I -> ~T given

(N /\ ~V) -> R goal

Then what happens when I, V, R, D are false and T, N are true?

If you can wait, I could look into this tomorrow morning. I like natural deduction! - Jan 11th 2010, 02:24 PMclic-clac
From what I see the problem is correct. (if I is false then R follows from the first given formula)

- Jan 12th 2010, 01:13 AMemakarov
If the parentheses are as I indicated and if I is false, the first formula is automatically true and does not say anything about R. I am not sure if I should try other ways to parenthesize or if there is something wrong with the problem statement...

- Jan 12th 2010, 02:19 AMclic-clac
Hell, true; I don't know why when I saw the first formula true I deduced R was true... And I made that mistake twice before posting :)

I don't know, I would have put the parentheses exactly as you did. Unless in the first formula, we have to read

$\displaystyle I\wedge (\neg(T\vee D)\rightarrow R)$ (but I find that strange)

the problem statement may be wrong. - Jan 12th 2010, 04:51 AMSavvascl
$\displaystyle

(I\wedge \neg(T\vee D)) \rightarrow R\:\:\: given $

$\displaystyle (D\wedge N) \rightarrow V \qquad\;\quad\: given $

$\displaystyle I \rightarrow \neg T \qquad\qquad\qquad given $

$\displaystyle (N\wedge \neg V ) \rightarrow R \qquad\quad goal

$

So thats more like!! The problem statements are correct I ve just put also the parentheses to make it easier to read.

(Anyone can eliminate the parentheses using the parenthesis elimination rules!!) ! So any ideas...?? - Jan 12th 2010, 05:35 AMemakarov
Is there a difference with the version I gave above?

- Jan 12th 2010, 02:07 PMSavvascl
No I just made it more readable....