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

Algebra.Com
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)   (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
RELATED QUESTIONS

Use an ordinary proof (not conditional or indirect) to solve the following arguments... (answered by RBryant,Edwin McCravy,math_tutor2020)
I.Use an ordinary proof (not conditional or indirect) to solve the following arguments.... (answered by Edwin McCravy)
Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by math_helper)
Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by jim_thompson5910)
Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by math_helper)
Use an ordinary proof (not conditional or indirect) to solve the following arguments. (answered by RBryant)
INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. (answered by AnlytcPhil)
INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. (answered by jim_thompson5910)
Use an ordinary proof (not conditional or indirect) to solve the following arguments... (answered by Edwin McCravy)