[SOLVED] Logic proof which I am having trouble understanding

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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.
June 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??
June 17th 2009, 03:51 PM
harihari

Thanks everyone, I worked it out
July 14th 2009, 10:24 PM
harihari

This exactly how the proof was given by the way but it has been explained now