document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043570>Question 1043570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Proof by Natural Deduction – Propositional Logic. Use a direct proof to show that the following argument is valid.\r<BR>\n" );
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document.write( "Premise 1: (E • I) v (M •U)<BR>\n" );
document.write( "Premise 2: ~E<BR>\n" );
document.write( "Conclusion: ~(E v ~M) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659044 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) ~E    --------------hypothesis<BR>\n" );
document.write( "2) ~E v ~I -------------addition<BR>\n" );
document.write( "3) ~(E•I)  -------------de Morgan's<BR>\n" );
document.write( "4) (E • I) v (M •U) ----hypothesis<BR>\n" );
document.write( "5) ~(E • I) -> (M •U) --material implication on #4<BR>\n" );
document.write( "6) M •U   -----------modus ponens by #3 and #5<BR>\n" );
document.write( "7)  M ---------------simplification<BR>\n" );
document.write( "8)  ~E • M  ----------conjunction, by #1 and #7<BR>\n" );
document.write( "9) ~(E v M) -----------de Morgan's  </SPAN>\n" );
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