Thread: Logic subproofs within subproofs

So I've been stuck on this problem for a while, trying different combinations of rules, but I can't figure it out. The problem is:

|A v B
|A v C
|__
|A v (B n C)

The n stands for 'and', and the lines are my attempt at a Fitch line.

So I need to use subproofs within subproofs, and introduction and elimination rules for negation, conjunction, disjunction and contradiction online. I can't cite DeMorgan's laws.

I would appreciate any help. Thank you!

Originally Posted by Parches

So I've been stuck on this problem for a while, trying different combinations of rules, but I can't figure it out. The problem is:
|A v B
|A v C
|__
|A v (B n C)

So I need to use subproofs within subproofs, and introduction and elimination rules for negation, conjunction, disjunction and contradiction online. I can't cite DeMorgan's laws.

I must ask: WHY NOT?
Otherwise, I do not understand this question.
Can you explain? Give us the exact question.

Oh, because one of the points of the exercise is that we can see where DeMorgan's laws come from, so we are not supposed to cite them for proofs. I suspect the teacher might go over these in class and tell us how we basically used the law without citing it.

But for this exercise, we are only allowed to cite introduction and elimination rules for negation, conjunction, disjunction and contradiction.

The exact question is: Use Fitch to give formal proofs for the following argument. You will need to use subproofs within subproofs to prove this.

Fitch is basically a proof software, so you can ignore that part.

Thanks again.

Originally Posted by Parches

The exact question is: Use Fitch to give formal proofs for the following argument. You will need to use subproofs within subproofs to prove this.
Fitch is basically a proof software, so you can ignore that part.

Well it seems to me that you and other 'Fitch' users are on your own on this one.

Are you telling me it's impossible?

I mean, there are formal proofs for DeMorgan's laws using only the rules I mentioned, so I'm thinking there's got to be a workaround for citing them. I just don't know how to do this.

Thanks.