Deriving rules of inference

• May 19th 2009, 11:55 AM
epicurean
Deriving rules of inference
I'm going over old test results, and for whatever reason I just can't get this one into my head.

Given the proposition

$(p \rightarrow q)\rightarrow(p \vee r \rightarrow q \vee r)$

determine whether it is a tautology
[it is, of course], and, if it is a tautology, write the valid argument determined by it.

In other words, figure out what rule of inference can be derived from this argument. I believe it is modus tollens, but am not sure, and just can't see what method I would use to go about this. Any ideas?

Thanks to all the good people out there!
• May 19th 2009, 01:09 PM
TheAbstractionist
Quote:

Originally Posted by epicurean
I'm going over old test results, and for whatever reason I just can't get this one into my head.

Given the proposition

$(p \rightarrow q)\rightarrow(p \vee r \rightarrow q \vee r)$

determine whether it is a tautology
[it is, of course], and, if it is a tautology, write the valid argument determined by it.

In other words, figure out what rule of inference can be derived from this argument. I believe it is modus tollens, but am not sure, and just can't see what method I would use to go about this. Any ideas?

Thanks to all the good people out there!

Hi epicurean.

Modus tollens is the tautology $((p\rightarrow q)\wedge\neg\,q)\rightarrow\neg\,p.$ I have no idea what your tautology is called.
• May 19th 2009, 03:30 PM
epicurean
Abstractionist,

Thanks for taking a look at it. Now that I look at it again, it appears to be much closer to Resolution, but still isn't quite right. Methinks it could bear more looking at from my side. Thanks again!