SOLUTION: 1. (O ⊃ R) ⊃ S 2. (P ⊃ R) ⊃ ~S / ~R

Question 1179977: 1. (O ⊃ R) ⊃ S
2. (P ⊃ R) ⊃ ~S / ~R

Answer by RBryant(14) (Show Source): You can put this solution on YOUR website!

1. (O ⊃ R) ⊃ S
2. (P ⊃ R) ⊃ ~S   /  ~R
----------------------------------------------------------
3. ~S ⊃ ~ (O ⊃ R)                       1,   Trans
4. (P ⊃ R) ⊃ ~ (O ⊃ R)                 2,3   H.S.
5. ~ (P ⊃ R) v ~ (O ⊃ R)                4    Impl
6. ~ (~P v R) v ~ (~O v R)               5    Impl
7. (~ ~P • ~R) v (~ ~O • ~R)             6    DeM
8. (P • ~R) v (O • ~R)                   7    D.N.
9. [(P • ~R) v O] • [(P • ~R) v ~R]      8    Dist
10. [(P • ~R) v ~R] • [(P • ~R) v O]     9    Comm
11. (P • ~R) v ~R                       10    Simp
12. ~R v (P • ~R)                       11    Comm
13. (~R v P) • (~R v ~R)                12    Dist
14. (~R v ~R) • (~R v P)                13    Comm
15. (~R v ~R)                           14    Simp
16. ~R                                  15    Taut
                                                   QED

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