SOLUTION: 1. (P v F) -> (A v D) 2. A -> (M ^ ~P) 3. D -> (C ^ ~P) / ~P

Algebra ->  Proofs -> SOLUTION: 1. (P v F) -> (A v D) 2. A -> (M ^ ~P) 3. D -> (C ^ ~P) / ~P      Log On


   

Question 1009889: 1. (P v F) -> (A v D)
2. A -> (M ^ ~P)
3. D -> (C ^ ~P) / ~P
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Indirect proof

 1. (P v F) -> (A v D)
 2. A -> (M ^ ~P)
 3. D -> (C ^ ~P)      / ~P

 4. ~~P                        AIP
 5. P                        4, DN 
 6. P v F                    5, add.
 7. A v D                  1,6, MP
 8. (M ^ ~P) v (C ^ ~P)  7,2,3, DE (disjunctive elimination)
 9. (M v C) ^ ~P             8, distribution
10. ~P ^ (M v C)             9, commutation
11. ~P                      10, simp.
12. P^~P                  5,11, conj.
13. ~P                    4-12  IP

Edwin