document.write( "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:\r
\n" ); document.write( "\n" ); document.write( "1. R->S given
\n" ); document.write( "2. P->Q given
\n" ); document.write( "3.[(PvK) & N]->(K->R) given
\n" ); document.write( "4. PvK given
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\n" ); document.write( "6.(PvK) & N 4,5 conj.
\n" ); document.write( "7.K->R 6,6 M.P.
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\n" ); document.write( "\n" ); document.write( "...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! \n" ); document.write( "

Algebra.Com's Answer #428105 by jim_thompson5910(35256) $\"\"$ $\"About$

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

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