1. C 2. (C & T) > ~T 3. (C & ~T) > T / T < > ~T 4. ~~T > ~(C & T) 2, Transposition 5. T > ~(C & T) 4, Double negation 6. T > (~C v ~T) 5, DeMorgan 7. ~T v (~C v ~T) 6, Material Implication 8. ~T v (~T v ~C) 7, Commutation 9. (~T v ~T) v ~C 8, Association 10. ~T v ~C 9, Tautology 11. ~C v ~T 10, Commutation 12. ~~C 1, Double Negation 13. ~T 11,12, Disjunctive Syllogism 14. C & ~T 1,13, Conjunction 15. T 3,14, Modus Ponens 16. T v T 15, Addition 17. ~~T v T 16, Double Negation 18. ~T > T 17, Material Implication 19. ~T v ~T 13, Addition 20. T > ~T 19, Material Implication 21. T < > ~T 20,18, Material Equivalence Edwin