# Help with Logic (Natural Deduction)

• Jan 11th 2010, 10:58 AM
Savvascl
Help 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 PM
emakarov
Quote:

I ^ ~(TvD) -> R given
D^N -> V given
I -> ~T given

N^~V -> R goal
I don't think it follows. I assume the parentheses are as follows:

(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 PM
clic-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 AM
emakarov
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 AM
clic-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

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

the problem statement may be wrong.
• Jan 12th 2010, 04:51 AM
Savvascl
$
(I\wedge \neg(T\vee D)) \rightarrow R\:\:\: given$

$(D\wedge N) \rightarrow V \qquad\;\quad\: given$
$I \rightarrow \neg T \qquad\qquad\qquad given$

$(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 AM
emakarov
Is there a difference with the version I gave above?
• Jan 12th 2010, 02:07 PM
Savvascl