document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150092>Question 1150092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	[A v (K & J)] > (~E &~F) <BR>\n" );
document.write( "2.	M > [A & (P v R)]<BR>\n" );
document.write( "3.	M & U                            /~E & A<BR>\n" );
document.write( "How do I continue? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771451 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=771451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "The conclusion has ~E and A. So we'll have to track down those terms. \r<BR>\n" );
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document.write( "We see \"A\" is buried in the second premise. To free it, we need to use modus ponens. So we'll need the antecedent M. Luckily line 3 has an M we need. Use the simplification rule to go from M&U to just M. We will never use the \"U\" that is part of line 3. This is likely a distraction your teacher has thrown in.\r<BR>\n" );
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document.write( "Once we have M, we can use modus ponens along with line 2 to get A & (P v R). Use simplification to reduce that to just A. The (P v R) is never used. Probably another distraction.\r<BR>\n" );
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document.write( "With \"A\" freed up, we can use the addition rule to add on any logical expression we want. Go from A to A v (K & J). This builds up the antecedent of premise 1, which helps free up ~E & ~F\r<BR>\n" );
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document.write( "Now use simplification yet again to get ~E.\r<BR>\n" );
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document.write( "Together with ~E and A, we'll use the conjunction rule to get the conclusion we are aiming for.\r<BR>\n" );
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document.write( "---------------------------------------------------<BR>\n" );
document.write( "Here's what the full derivation looks like<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
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document.write( "<tr><TD >Number</TD><TD >Statement</TD><TD >Line(s) Used</TD><TD >Reason</TD></tr>\r\n" );
document.write( "<tr><TD >1</TD><TD >[A v (K & J)] > (~E & F)</TD><TD ></TD><TD ></TD></tr>\r\n" );
document.write( "<tr><TD >2</TD><TD >M > [A & (P v R)]</TD><TD ></TD><TD ></TD></tr>\r\n" );
document.write( "<tr><TD >3</TD><TD >M & U</TD><TD ></TD><TD ></TD></tr>\r\n" );
document.write( "<tr><TD >:.</TD><TD >~E & A</TD><TD ></TD><TD ></TD></tr>\r\n" );
document.write( "<tr><TD >4</TD><TD >M</TD><TD >3</TD><TD >Simp</TD></tr>\r\n" );
document.write( "<tr><TD >5</TD><TD >A & (P v R)</TD><TD >2,4</TD><TD >MP</TD></tr>\r\n" );
document.write( "<tr><TD >6</TD><TD >A</TD><TD >5</TD><TD >Simp</TD></tr>\r\n" );
document.write( "<tr><TD >7</TD><TD >A v (K & J)</TD><TD >6</TD><TD >Add</TD></tr>\r\n" );
document.write( "<tr><TD >8</TD><TD >~E & F</TD><TD >1,7</TD><TD >MP</TD></tr>\r\n" );
document.write( "<tr><TD >9</TD><TD >~E</TD><TD >8</TD><TD >Simp</TD></tr>\r\n" );
document.write( "<tr><TD >10</TD><TD >~E & A</TD><TD >9,6</TD><TD >Conj</TD></tr>\r\n" );
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document.write( "Abbreviations Used:<BR>\n" );
document.write( "Add = Addition<BR>\n" );
document.write( "Conj = Conjunction<BR>\n" );
document.write( "MP = Modus Ponens<BR>\n" );
document.write( "Simp = Simplification\r<BR>\n" );
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document.write( "The rules of addition, conjunction, modus ponens and simplification are part of a group of logic rules of inference. <BR>\n" );
document.write( "For more information, check out the link below<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www2.cs.duke.edu/courses/summer13/compsci230/restricted/lectures/L05.pdf\">https://www2.cs.duke.edu/courses/summer13/compsci230/restricted/lectures/L05.pdf</a><BR>\n" );
document.write( "(the specific rules are found on pages 5, 9, 10, and 11)<BR>\n" );
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