# [SOLVED] Logic proof which I am having trouble understanding

• May 30th 2009, 03:59 AM
harihari
[SOLVED] Logic proof which I am having trouble understanding
We have been given the following as an example of a proof, but I can not follow it.
(b(1)=C OR b(1) ≠ C) AND (b(1)=C AND b(2)=J OR b(1)=J AND b(2)=C), (b(1)=C AND b(1) = J)=F
--------------------------------------...
(b(1)=C AND b(2)=J) OR (b(1) ≠ C) AND (b(1)=J AND b(2)=C)
--------------------------------------...
b(1) ≠ C OR b(2) = J
-------------------------------------
b(1) = C -> b(2) = J

I see what happens from the second to last step but I'm unsure about the rest. Could someone please explain? Thanks
• May 30th 2009, 02:58 PM
Danneedshelp
I think for the last step, the writter just used the fact that $(\sim P) \vee Q \Leftrightarrow P \Rightarrow Q$.
• May 30th 2009, 03:05 PM
Danneedshelp
Note: I am not sure why the first statement $(B(1)=C \vee B(1) \neq C)$ stuck around, because $P \vee(\sim P)$ is a tautology.
• Jun 5th 2009, 06:57 PM
xalk
Quote:

Originally Posted by harihari
We have been given the following as an example of a proof, but I can not follow it.
(b(1)=C OR b(1) ≠ C) AND (b(1)=C AND b(2)=J OR b(1)=J AND b(2)=C), (b(1)=C AND b(1) = J)=F
--------------------------------------...
(b(1)=C AND b(2)=J) OR (b(1) ≠ C) AND (b(1)=J AND b(2)=C)
--------------------------------------...
b(1) ≠ C OR b(2) = J
-------------------------------------
b(1) = C -> b(2) = J

I see what happens from the second to last step but I'm unsure about the rest. Could someone please explain? Thanks

CAN you write more clearly the proof you are given as an example in steps,because the way the proof is given makes no sense.

WHAT IS given and what is the conclusion here??
• Jun 17th 2009, 03:51 PM
harihari
Thanks everyone, I worked it out
• Jul 14th 2009, 10:24 PM
harihari
This exactly how the proof was given by the way but it has been explained now