SOLUTION: i need help solving this indirect proof 1. (R v S) > (H & ~G) 2. (K v R) > (G v ~H) / ~R and also help on a conditional proof 1. N > (F & A) 2. B > (R & F) /

Algebra ->  Proofs -> SOLUTION: i need help solving this indirect proof 1. (R v S) > (H & ~G) 2. (K v R) > (G v ~H) / ~R and also help on a conditional proof 1. N > (F & A) 2. B > (R & F) /      Log On


   

Question 1008769: i need help solving this indirect proof
1. (R v S) > (H & ~G)
2. (K v R) > (G v ~H) / ~R
and also help on a conditional proof
1. N > (F & A)
2. B > (R & F) / (N v B) > (A v R)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 1. (R v S) > (H & ~G)
 2. (K v R) > (G v ~H)     /   ~R

 3.  ~~R                   Indirect Proof Assumption (IPA)
 4. R                      3, Double Negation        (DN)
 5. R v S                  4, Addition               (Add)
 6. H & ~G                 1,5, Modus Ponens         (MP)
 7. ~G & H                 6, Commutativity          (Comm)
 8. ~G & ~~H               7, Double Negation        (DN)
 9. ~(G v ~H)              8, DeMorgan's Law         (DM)
10. ~(K v R)               2,9 Modus Tollens         (MT)
11. ~K & ~R                10, DeMorgan's Law        (DM)
12. ~R                     11, Simplification        (Simp)
13. R & ~R                 4,13 Conjunction          (Conj)
14. ~R                     3-13 Indirect Proof       (IP)       

and also help on a conditional proof
1. N > (F & A)
2. B > (R & F)       /    (N v B) > (A v R)

3. N v B                Conditional Proof Assumption    (CPA)
4. (F & A) v (R & F)    1,2,3 Constructive Dilemma      (CD)
5. (F & A) v (F & R)    4, Commutativity                (Comm) 
6. F & (A v R)          5, Distribution                 (Dist)
7. A v R                6, (Conjunctive) Simplification (Simp)  
8. (N v B) > (A v R)    3-7 Conditional Proof           (CP)   

Edwin