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Assignment 2 - Question 2.2

Posted by rezrovs 
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Assignment 2 - Question 2.2
April 20, 2008 11:21PM
Hi there

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)
2. Tet(b)
----
3.1 b = c
----
3.2 Cube(b) v Dodec(b)

3.2.1.1 Cube(b)
----
3.2.1.2 (contradiction)
3.2.1.3 ~(b = c)

3.2.2.1 Dodec(b)
----
3.2.2.2 (contradiction)
3.2.2.3 ~(b = c)

3.3 (contradiction)

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.

Thanks,
Rachel

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?
Re: Assignment 2 - Question 2.2
May 21, 2008 02:24PM
Hi Racchel

Which rule did you cite in support of 3.2.1.2
Re: Assignment 2 - Question 2.2
May 21, 2008 03:07PM
Hi there

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 3.2.1.1 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.
Re: Assignment 2 - Question 2.2
May 21, 2008 08:14PM
Hi again

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...
Re: Assignment 2 - Question 2.2
May 22, 2008 10:00AM
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 ...
Re: Assignment 2 - Question 2.2
May 22, 2008 10:07AM
I'm pretty sure that AnaCon is in the section that we're supposed to cover for the assignment. So I'm sure that means we can use it.

What makes you think that we can't?
Anonymous User
Re: Assignment 2 - Question 2.2
May 22, 2008 11:48AM
Ana Con is a "shortcut" used in special cases. They want us to use the proofs.
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