Proving set inconsistency in SD and deriving ¬H

[gabwind]

Hi, I am having trouble showing that
{F > ~ G. ~ F > ~H, (~ F v G) & H}
is inconsistent in SD.

Also I don't understand how one can derive: ~ H
from: {(R v ~ H), (~ R v ~ H)}


I would be grateful to anyone who can help me understand these problems.

 

[whozum]

For both you need to make provisional assumptions and show that either the assumption yields an inconsistency in the proof (introduced by the assumption) or validates it. For #2, I would make the assumption R.

 

[honestrosewater]

If you still have trouble, here's a few step to get you started:
1. F -> ~G
2. ~F -> ~H
3. (~F v G) & H
4. ~F v G [3, Simplification]
5. ~F v ~G [1, Implication]
6. (~F v G) & (~F v ~G) [4, 5, Conjunction]
7. ~F v (G & ~G) [6, Distribution]
8. ... assumption time

1. R v ~H
2. ~R v ~H
3. (R v ~H) & (~R v ~H) [1, 2, Conjunction]
4. ... does 3 look familiar?