SOLUTION: Use an ordinary proof (not conditional or indirect) to solve the following arguments. 1. (O ⊃ R) ⊃ S 2. (P ⊃ R) ⊃ ~S/ ~R

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Question 1179973: Use an ordinary proof (not conditional or indirect) to solve the following arguments.
1. (O ⊃ R) ⊃ S
2. (P ⊃ R) ⊃ ~S/ ~R
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 1. (O ⊃ R) ⊃ S
 2. (P ⊃ R) ⊃ ~S/ ~R

 3. ~~S ⊃ ~(P ⊃ R)        2, transposition
 4. S ⊃ ~(P ⊃ R)          3, double negation
 5. (O ⊃ R) ⊃ ~(P ⊃ R)    1,4, hypothetical syllogism
 6. (~O v R) ⊃ ~(P ⊃ R)   5, material implication
 7. (~O v R) ⊃ ~(~P v R)   6, material implication    
 8. (~O v R) ⊃ (~~P • ~R)  7, deMorgan's law
 9. (~O v R) ⊃ (P • ~R)    8, material implication
10. ~(~O v R) v (P • ~R)   9, material implication
11. (~~O • ~R) v (P • ~R)  10, deMorgan's law
12. (O • ~R) v (P • ~R)    11, double negation
13. (O v P) • ~R           12, distribution
14. ~R • (O v P)           13, commutation
15. ~R                     14, simplification

Edwin