# Thread: Arguments - Inference laws problem

1. ## [SOLVED] Arguments - Inference laws problem

[SOLVED] THANKS

Hi,
I just found this forum and it looks pretty nice.

I can't seem to be able to justify #1 (It's invalid, I have the answer, but I can't figure out how to justify it)

About #2, well I just can't figure it out. I don't even know if it's valid or not... let alone justifying it.

I would really appreciate your help.
Thank you

2. Originally Posted by Zathan
Hi,
I just found this forum and it looks pretty nice.

I can't seem to be able to justify #1 (It's invalid, I have the answer, but I can't figure out how to justify it)

About #2, well I just can't figure it out. I don't even know if it's valid or not... let alone justifying it.

I would really appreciate your help.
Thank you

For #1), to establish invalidity you'll need to come up with a structure that makes the premisses simultaneously true and the conclusion false.
Consider a structure that makes p true, r false, and q false.

For #2), most textbooks (if they refer to it at all) call that form (or a slightly massaged version of it), complex constructive dilemma.
It's certainly a valid argument. But, I think you'll need to be clear about what you mean by "justifying it".

A semantic approach isn't too bad here, since there is only one way to make the conclusion false.
That of course fixes the truth-values for q and s. Now all you have to do is fiddle around with p and r in an attempt to make the premisses true. You'll quickly see that any such attempt is futile.

Of course in a logic equipped with a deductive apparatus, say a typical NDS, you could just carry out a formal derivation. The derivation will require a few steps, if you restrict yourself to working only with the normal prime rules of inference.
In this context, another thing to consider is what should be taken for VE as a prime rule.
Some texts take a rule version of simple constructive dilemma as their VE; on the other hand, some take disjunctive syllogism.
I'd say your free to choose. Which one might be best suited for a derivation of #2?