# SOLUTION: Can you help me with this proof? (O>R)>S / (P>R)~S // ~R The > is a horseshoe. I've been at this all day and I can't even think of how to start.

Algebra ->  Algebra  -> Proofs -> SOLUTION: Can you help me with this proof? (O>R)>S / (P>R)~S // ~R The > is a horseshoe. I've been at this all day and I can't even think of how to start.      Log On

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 Logic: Proofs Solvers Lessons Answers archive Quiz In Depth

 Question 593872: Can you help me with this proof? (O>R)>S / (P>R)~S // ~R The > is a horseshoe. I've been at this all day and I can't even think of how to start.Answer by jim_thompson5910(28593)   (Show Source): You can put this solution on YOUR website!```1. (O > R) > S 2. (P > R) > ~S // ~R ------------------------------------------------------- 3. (~O v R) > S 1 MI 4. ~(~O v R) v S 3 MI 5. (~~O & ~R) v S 4 DM 6. (O & ~R) v S 5 DN 7. S v (O & ~R) 6 Comm 8. (S v O) & (S v ~R) 7 Dist 9. (S v ~R) & (S v O) 8 Comm 10. S v ~R 9 Simp 11. ~R v S 10 Comm 12. R > S 11 MI 13. ~S > ~R 12 Trans 14. (~P v R) > ~S 2 MI 15. ~(~P v R) v ~S 14 MI 16. (~~P & ~R) v ~S 15 DM 17. (P & ~R) v ~S 16 DN 18. ~S v (P & ~R) 17 Comm 19. (~S v P) & (~S v ~R) 18 Dist 20. (~S v ~R) & (~S v P) 19 Comm 21. ~S v ~R 20 Simp 22. ~R v ~S 21 Comm 23. R > ~S 22 MI 24. R > ~R 23,13 HS 25. ~R v ~R 24 MI 26. ~R 25 Taut ``` Notes: The abbreviations used are... MI: Material Implication DM: De Morgan's Law DN: Double Negation Dist: Distribution Comm: Commutation Simp: Simplification Trans: Transposition HS: Hypothetical Syllogism Taut: Tautology