You step 8 is incorrect. Here's how I would do it: 1. DvM 2. M-->R 3. Sv(Q&X) 4. R-->~S 5. ~D /Q 6. M 1,5 DS (disjunctive syllogism) 7. R 2,6 MP (modus ponens) 8. ~S 4,7 MP (modus ponens) 9. Q&X 3,8 DS (disjunctive syllogism) 10. Q 9,simp (simplification) Edwin