document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029123>Question 1029123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> COMPLETE THE FOLLOWING PROOFS USING CONDITIONAL PROOF\r<BR>\n" );
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document.write( "Premises:<BR>\n" );
document.write( "1. G &#8835; (E &#8835; N)<BR>\n" );
document.write( "2. H &#8835; (~N &#8835; E)<BR>\n" );
document.write( "Conclusion:<BR>\n" );
document.write( "G &#8835; ( H &#8835; N)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644203 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=644203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  G &#8835; (E &#8835; N)--------------Hypothesis<BR>\n" );
document.write( "2.  (G&#8743;E)&#8835;N -----------------------Exportation<BR>\n" );
document.write( "3. (E&#8743;G)&#8835;N------------------Commutativity<BR>\n" );
document.write( "4. E&#8835;(G&#8835;N)------------------Exportation<BR>\n" );
document.write( "5. H &#8835; (~N &#8835; E)---------------Hypothesis<BR>\n" );
document.write( "6. H&#8835;(~E&#8835;N)-----------------Contraposition on part of #5<BR>\n" );
document.write( "7. (~E&#8743;H)&#8835;N------------------Exportation, and the Commutativity<BR>\n" );
document.write( "8. ~E&#8835;(H&#8835;N)-----------------Exportation<BR>\n" );
document.write( "9. ~(H&#8835;N)&#8835;E -----------------Contrapositive of #8<BR>\n" );
document.write( "10. ~(H&#8835;N)&#8835;(G&#8835;N)----#4 and #9, and hypothetical syllogism<BR>\n" );
document.write( "11. (H&#8743;~N)&#8835;(G&#8835;N)----Negative of material implication & de Morgan's law<BR>\n" );
document.write( "12. H&#8835;(~N&#8835;(G&#8835;N)------Exportation<BR>\n" );
document.write( "13.  H&#8835;(~~N&#8744;~G&#8744;N)-----Material implication<BR>\n" );
document.write( "14.   H&#8835;(~G&#8744;N)----------- Double negation and N&#8744;N&#8801; N<BR>\n" );
document.write( "15.   H&#8835;(G&#8835;N)--------------Material implication<BR>\n" );
document.write( "16.  (H&#8743;G)&#8835;N---------------Exportation<BR>\n" );
document.write( "17.   G&#8835;(H&#8835;N)---------------Commutativity and exportation </SPAN>\n" );
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