1. (R v S) -> (T & U) 2. ~R -> (V -> ~V) 3. ~T /Therefore ~V ------------------------------------------ 4. ~T v ~U 3 Addition 5. ~(T & U) 4 De Morgan's Law 6. ~(R v S) 1,5 Modus Tollens 7. ~R & ~S 6 De Morgan's Law 8. ~R 7 Simplification 9. V -> ~V 2,8 Modus Ponens 10. ~V v ~V 9 Material Implication 11. ~V 10 Tautology