SOLUTION: I'm having a ton of trouble figuring out this proof for our take-home quiz. We're only supposed to use the first 8 rules of solving propositional logic, which include modus ponens,

Question 694575: I'm having a ton of trouble figuring out this proof for our take-home quiz. We're only supposed to use the first 8 rules of solving propositional logic, which include modus ponens, modus tollens, constructive dilemma, hypothetical syllogism, disjunctive syllogism, simplification, conjunction, and addition. Here's what I have so far:
1. R->S given
2. P->Q given
3.[(PvK) & N]->(K->R) given
4. PvK given
5.N given
6.(PvK) & N 4,5 conj.
7.K->R 6,6 M.P.
8.K->S 1,7 H.S.
...and that's where I get stuck. Any help would be great. I'm trying to reach a conclusion of QvS, which makes me think the last few steps are going to be constructive dilemma but it's really difficult to get there. Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You're doing great until you hit line 8, here's one way how you do it

1. R->S                         given
2. P->Q                         given
3.[(PvK) & N]->(K->R)           given
4. PvK                          given
5. N                            given
--------------------------------------
6.  (P v K) & N                  4,5   Conj
7.  K -> R                       3,6   MP
8.  K v P                        4     Comm
9.  ~~K v P                      6     DN
10. ~K -> P                      7     MI
11. ~P -> ~~K                    10    Trans
12. ~P -> K                      11    DN
13. ~P -> R                      12,7  HS
14. ~~P v R                      13    MI
15. P v R                        14    DN
16. (P -> Q) & (R -> S)          2,1   Conj
17. Q v S                        16,15 CD

Edit: I realized that you can only use the first 8 rules. Here is the fixed version. In this version you are so close that you just need two more lines.

Much easier version...

1. R->S                         given
2. P->Q                         given
3.[(PvK) & N]->(K->R)           given
4. PvK                          given
5. N                            given
--------------------------------------
6.  (P v K) & N                  4,5   Conj
7.  K -> R                       3,6   MP
8.  K -> S                       7,1   HS
9.  (P -> Q) & (K -> S)          2,8   Conj
10.  Q v S                       9,4   CD

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