1. (H . S) > [ H > (C > W)]

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Presentation transcript:

1. (H . S) > [ H > (C > W)] 3. H ACP S MP 3, 2 H . S CN 3,4 6. H > ( C > W) MP 1,5 7. C > W MP 3, 6 8. H > (C > W) CP 3-7

C > (A . D) B > (A . E) / (C v B) > A 3. C v B ACP 4. [C > (A . D)] . [B > (A . E)] CN 1,2 5. (A . D) v (A . E) CD 3,4 6. A . (D v E) DIST 5 7. A SM 6 8. (C v B) > A CP 3-7

C > (D v ~E) E > (D > F) / C > (E > F) 3. C ACP 4. E ACP 5. D v ~E MP 1,3 6. D > F MP 2,4 ~ D > ~E IMP 5 E > D TRAN 7 E > F HS 8,6 10. F MP 4, 9 11. E > F CP 4-10 12. C > (E > F) CP 3-11

Indirect Proof Reductio ad absurdem Assume the conclusion is false, and show that that assumption leads to a necessarily false statement -- a self-contradiction. This proves that the assumption is false, which means the originally proposed conclusion is true. 1. (S v T) > ~S / ~S 2. ~ ~S AIP 3. ~ (S v T) MT 1,2 4. ~S . ~T DM 3 5. ~ S SM 4 6. S . ~S DN, CN 2,5 7. ~S IP 2-6

S > (T v ~U) U > (~T v R) (S .U) > ~R /~S v ~U 4. ~( ~S v ~U) AIP 5. S . U DM 4 6. S SM 5 7. U CM, SM 5 8. ~R MP 5, 3 9. ~T v R MP 2, 7 10. ~T CM, DS 8, 9 11. T v ~U MP 1,6 12. ~U DS 10,11 13. U . ~U CN 7, 12 14. ~S v ~U IP 4-13