document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=593872>Question 593872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with this proof?<BR>\n" );
document.write( "(O>R)>S / (P>R)~S // ~R\r<BR>\n" );
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document.write( "The > is a horseshoe. I've been at this all day and I can't even think of how to start. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376502 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=376502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "1.  (O > R) > S\r\n" );
document.write( "2.  (P > R) > ~S    // ~R\r\n" );
document.write( "-------------------------------------------------------\r\n" );
document.write( "3.  (~O v R) > S                       1       MI\r\n" );
document.write( "4.  ~(~O v R) v S                      3       MI\r\n" );
document.write( "5.  (~~O & ~R) v S                     4       DM\r\n" );
document.write( "6.  (O & ~R) v S                       5       DN\r\n" );
document.write( "7.  S v (O & ~R)                       6       Comm\r\n" );
document.write( "8.  (S v O) & (S v ~R)                 7       Dist\r\n" );
document.write( "9.  (S v ~R) & (S v O)                 8       Comm\r\n" );
document.write( "10.  S v ~R                            9       Simp\r\n" );
document.write( "11.  ~R v S                            10      Comm\r\n" );
document.write( "12.  R > S                             11      MI\r\n" );
document.write( "13.  ~S > ~R                           12      Trans\r\n" );
document.write( "14. (~P v R) > ~S                      2       MI\r\n" );
document.write( "15. ~(~P v R) v ~S                     14      MI\r\n" );
document.write( "16. (~~P & ~R) v ~S                    15      DM\r\n" );
document.write( "17. (P & ~R) v ~S                      16      DN\r\n" );
document.write( "18. ~S v (P & ~R)                      17      Comm\r\n" );
document.write( "19. (~S v P) & (~S v ~R)               18      Dist\r\n" );
document.write( "20. (~S v ~R) & (~S v P)               19      Comm\r\n" );
document.write( "21. ~S v ~R                            20      Simp\r\n" );
document.write( "22. ~R v ~S                            21      Comm\r\n" );
document.write( "23. R > ~S                             22      MI\r\n" );
document.write( "24. R > ~R                             23,13   HS\r\n" );
document.write( "25. ~R v ~R                            24      MI\r\n" );
document.write( "26. ~R                                 25      Taut\r\n" );
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document.write( "Notes: The abbreviations used are...\r<BR>\n" );
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document.write( "MI: Material Implication<BR>\n" );
document.write( "DM: De Morgan's Law<BR>\n" );
document.write( "DN: Double Negation<BR>\n" );
document.write( "Dist: Distribution<BR>\n" );
document.write( "Comm: Commutation<BR>\n" );
document.write( "Simp: Simplification<BR>\n" );
document.write( "Trans: Transposition<BR>\n" );
document.write( "HS: Hypothetical Syllogism<BR>\n" );
document.write( "Taut: Tautology </SPAN>\n" );
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