SOLUTION: how to solve using indirect proof when there is a conditional in the conclusion 1. (AvD) -> M 2. ~(BvO) 3. R<->(O.T) 4. ~R<->A :. ~(M->O)

Algebra ->  Proofs -> SOLUTION: how to solve using indirect proof when there is a conditional in the conclusion 1. (AvD) -> M 2. ~(BvO) 3. R<->(O.T) 4. ~R<->A :. ~(M->O)       Log On


   

Question 1061899: how to solve using indirect proof when there is a conditional in the conclusion
1. (AvD) -> M
2. ~(BvO)
3. R<->(O.T)
4. ~R<->A :. ~(M->O)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1. (AvD) -> M
2. ~(BvO)
3. R<->(O.T)
4. ~R<->A      :. ~(M->O)

             |5. ~~(M->O)                   AIP
             |6. M->O                     15, DN
             |7. ~B&~O                     2, DM
             |8. ~O&~B                     7, comm
             |9. ~O                        8, simp
             |10. ~M                     6,9, MT               
             |11. ~(AvD)                1,10, MT
             |12. ~A&~D                   11, DM   
             |13. ~A                      12, simp
             |14. (~R->A)&(A->~R)          4, ME
             |15. ~R->A                   14, simp
             |16. ~~R                  15,13, MT  
             |17. R                       16, DN
             |18. [R->(O&T)]&[(O.T)->R]    3, ME
             |19. R->O&T                  18, simp
             |20. O&T                  19,17, MP
             |21. O                       20, simp
             |22. O&~O                  21,9, conj
 23. ~(M->O)           lines 5-22  IP 

Edwin