SOLUTION: SOLVE THE PROOF P v Q, P → (T → S), P → T, S ↔ Q ├ S 1. P v Q ASSUMPTION 2. P → (T → S) ASSUMPTION 3. P → T ASSUMPTION 4. S

Algebra ->  Proofs -> SOLUTION: SOLVE THE PROOF P v Q, P → (T → S), P → T, S ↔ Q ├ S 1. P v Q ASSUMPTION 2. P → (T → S) ASSUMPTION 3. P → T ASSUMPTION 4. S       Log On


   

Question 1155652: SOLVE THE PROOF
P v Q, P → (T → S), P → T, S ↔ Q ├ S
1. P v Q ASSUMPTION
2. P → (T → S) ASSUMPTION
3. P → T ASSUMPTION
4. S ↔ Q ASSUMPTION



CONCLUSION- S
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1.  P v Q   
2.  P → (T → S),  
3.  P → T,  
4.  S ↔ Q          ├  S

               |5.  ~S                  Assumption for Indirect Proof
               |6.  (S → Q) & (Q → S)     4,  Material Equivalence
               |7.  (Q → S) & (S → Q)     6,  Commutation
               |8.  Q → S                 7,  Simplification
               |9.  ~Q                  8,5,  Modus Tollens
               |10. Q v P                 1,  Commutation
               |11. P                  10,9,  Disjunctive Syllogism
               |12. T                   3,11, Modus Ponens    
               |13. T → S               2,11, Modus Ponens
               |14. S                  13,12, Modus Ponens
               |15. ~S & S              5,14, Conjunction
16. S                                 Lines 5-15 Indirect Proof

Edwin