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: