document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=531393>Question 531393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hey can you help me with these proofs? \r<BR>\n" );
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document.write( "1. ~(J & K)                 prem<BR>\n" );
document.write( "2. ~(L & M)                 prem<BR>\n" );
document.write( "3.   J v L / ~(K & M)       prem/conc<BR>\n" );
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document.write( "8.\r<BR>\n" );
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document.write( "1.~ P v Q                prem<BR>\n" );
document.write( "2.~ R > ~Q               prem<BR>\n" );
document.write( "3.~(R & ~S) / P > S      prem / conc<BR>\n" );
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document.write( "8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524961 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=524961\">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. ~(J & K) prem\r\n" );
document.write( "2. ~(L & M) prem\r\n" );
document.write( "3. J v L / ~(K & M) prem/conc\r\n" );
document.write( "4. ~J v ~K                            1    DM\r\n" );
document.write( "5. ~L v ~M                            2    DM\r\n" );
document.write( "6. J -> ~K                            4    MI\r\n" );
document.write( "7. L -> ~M                            5    MI\r\n" );
document.write( "8. (J -> ~K) & (L -> ~M)              6,7  Conj\r\n" );
document.write( "9. ~K v ~M                            8,3  CD\r\n" );
document.write( "10. ~(K & M)                          9    DM\r\n" );
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document.write( "Abbreviations/Acronyms Used:\r<BR>\n" );
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document.write( "CD = Constructive Dilemma<BR>\n" );
document.write( "Conj = Conjunction<BR>\n" );
document.write( "MI = Material Implication<BR>\n" );
document.write( "DM = De Morgan's Law\r<BR>\n" );
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document.write( "1.  ~P v Q prem\r\n" );
document.write( "2.  ~R > ~Q prem\r\n" );
document.write( "3.  ~(R & ~S) / P > S prem / conc\r\n" );
document.write( "4.  ~~Q > ~~R                       2     Trans\r\n" );
document.write( "5.  Q > R                           4     DN\r\n" );
document.write( "6.  P > Q                           1     MI\r\n" );
document.write( "7.  P > R                           6,5   HS\r\n" );
document.write( "8.  ~R v ~~S                        3     DM\r\n" );
document.write( "9.  ~R v S                          8     DN\r\n" );
document.write( "10. ~~R > S                         9     MI                         \r\n" );
document.write( "11. R > S                           10    DN\r\n" );
document.write( "12. P > S                           7,11  HS\r\n" );
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document.write( "Abbreviations/Acronyms Used:\r<BR>\n" );
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document.write( "Trans = Transposition<BR>\n" );
document.write( "DN = Double Negation<BR>\n" );
document.write( "MI = Material Implication<BR>\n" );
document.write( "HS = Hypothetical Syllogism<BR>\n" );
document.write( "DM = De Morgan's Law </SPAN>\n" );
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