I've been working on this question for most of yesterday and all of this evening and I'm stuck. I'm using Fitch to tell me if the proof is right and I just can't seem to get it.
I've tried to use two subproofs, one for Cube(c) and one for Dodec(c) but I don't get anywhere with that. Then I tried a subproof for the assumption of b=c, which I can get to a contradiction but then I don't know what to do next.
1. Cube(c) v Dodec(c)
3.1 b = c
3.2 Cube(b) v Dodec(b)
220.127.116.11 ~(b = c)
18.104.22.168 ~(b = c)
4. ~(b = c)
Fitch doesn't like the steps 3.3 and 4. And I also have a feeling I'm going about this all wrong - because this question is worth 8 points in comparison to 2.1 being worth 10 points, which I did in fewer steps than this...
Please could someone point me in the right direction.
PS: does anyone know where I can find out more about the error messages that you see when you get a reason wrong in Fitch?
I'm without my notes at the moment so I don't know the real name of the rule but I can tell the the basic idea I was going for.
In line 2, we are told that b is a tetrahedron. So in 22.214.171.124 of the proof where I say that b is a cube, I can say that this is a contradiction because b cannot be a cube if we are told that it is a tetrahedron.
I see where you're going(and agree on your reasoning), but I don't think you can prove it that way...
On P158 of the textbook it states that Fitch won't allow you a contradiction if it depends on the meaning of predicates other than identity. The book uses the example Cube(b) and Tet(b). It states you may use AnaCon. I don't think we are allowed to use any of the Cons in the assignments/exam though, so I have no idea how to proceed.
I am currently trying exercise 6.14, which is much the same idea I think, and have the same problem...
I took the approach of using Ana Con as I couldn't get a Fitch to accept any other rules however my proof was a little bit different in that I used \/ elimination to prove the conclusion ~(b = c). I do hope you're wrong about not being allowed to use Ana Con in the assignments ...