SOLUTION: 1. (E→~K) 2. (M∨(~K.~H)) 3. (~M∨E) .: ~K Construct a proof to show that the following argument is valid. You can use any proof technique you like, but you may find indirec

Algebra ->  Proofs -> SOLUTION: 1. (E→~K) 2. (M∨(~K.~H)) 3. (~M∨E) .: ~K Construct a proof to show that the following argument is valid. You can use any proof technique you like, but you may find indirec      Log On


   

Question 1208888: 1. (E→~K)
2. (M∨(~K.~H))
3. (~M∨E) .: ~K
Construct a proof to show that the following argument is valid. You can use any proof technique you like, but you may find indirect proof helpful.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

1. (E → ~K)
2. (M ∨ ( ~K ∙ ~H))
3. (~M ∨ E)         .: ~K

          |4.  ~~K      assumption for indirect proof
          |5.  ~E       1,4, transposition
          |6.  E ∨ ~M     3, commutation
          |7.  ~M       6,5, disjunctive syllogism
          |8.  ~K ∙ ~H  2,7, disjunctive syllogism
          |9.  ~K         8, simplification
          |10. ~K ∙ ~~K 9,4, conjunction

11.  ~K    lines 4-10 for indirect proof

Edwin