# Tautalogical Consequence

1. Sep 16, 2007

### ETuten

I am in needof help with the following problem:

Premises : Cube(a) v Cube(b)
Dodec(c) v Dodec(d)
~Cube(a) v ~Dodec(c)

Conclusion: Cube(b) v Dodec(d)

I need to add a sentence to the proof that is tautalogical consequence of two of the premises. I just can't see how to make such a deduction. Any help would be much appreciated

2. Sep 16, 2007

### MathematicalPhysicist

well it's quite immediate if take into account material conditional and destructive dillema:
~cube(a)->cube(b)
~dodec(c)->dodec(d)
~Cube(a) v ~Dodec(c)
so from DD you get the conclusion.
but let's say for the sake of argument that you can't use it here, so:
so what about ((Cube(a)vCube(b))->(Dodec(c)vDodec(d))->(~Cube(a)v~Dodec(c))->(Cube(b)vDodec(d))
you only need to check that then next thing is a tautology, quite long:
((~P->Q)->(~R->S)->(P->R)->(~Q->~S))
but as you might see it's all equivalent.

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