Thread: 'Proof', is my answer right? Plz check.

Question -

Use the rule of interface to show that if A, B, C and D are proposition, the conclusion C or ~D can be interred from the four hypotheses A=>B, B=> ~D, A, and B=>C.
The 'rules' are whether they are Modues ponens, Modus Tollens, Addition, Simplification, Conjuction or Hypothetical syllogism.


My answer -
A=>B, B=> ~D, A, and B=>C.

A, and A ===>B, therefore B

B in turns implies C on one hand and ~D on the other, hence implies C and ~D and
in particular C or ~D.

Is above answer right?

Thanks,
Oz

Seems about right
1. A->B (premise)
2. A (premise)
3. B (modus ponens 1, 2)
4. B->C (premise)
5. C (modus ponens 3, 4)
6. B->~D (premise)
7. ~D (modus ponens 3, 6)

Originally Posted by Skids

Seems about right
1. A->B (premise)
2. A (premise)
3. B (modus ponens 1, 2)
4. B->C (premise)
5. C (modus ponens 3, 4)
6. B->~D (premise)
7. ~D (modus ponens 3, 6)

I believe the conclusion should be C or notD and not only notD

Originally Posted by xalk

I believe the conclusion should be C or notD and not only notD

It is. Both C (line 5) and (line 7) ~D are valid conclusions and I have them up there.
I guess I could have put a further line
8. C ^ ~D but it didn't seem necessary.

Originally Posted by Skids

It is. Both C (line 5) and (line 7) ~D are valid conclusions and I have them up there.
I guess I could have put a further line
8. C ^ ~D but it didn't seem necessary.

It is: C or notD and not C and notD ,and we are not allowed to use Disjunction Introduction

Originally Posted by xalk

It is: C or notD and not C and notD ,and we are not allowed to use Disjunction Introduction

I'm not sure who this unstated 'we' is. I only showed that both C and ~D could be derived using the given premises. If you disagree, show where the derivation is wrong. Both are true under the premises and all that as far as I can see. I guess trying to help out is frowned up around here. I'll pack my swag and leave so that you (as in the unstated we) can be happy that Disjunction are not introduced. Something I didn't do. Goodbye.