document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194113>Question 1194113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 55.\r<BR>\n" );
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document.write( "1. (L ≡ N) ⊃ C\r<BR>\n" );
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document.write( "2. (L ≡ N) v (P ⊃ ~E)\r<BR>\n" );
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document.write( "3. ~E ⊃ C\r<BR>\n" );
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document.write( "4. ~C /~P\r<BR>\n" );
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document.write( "56.\r<BR>\n" );
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document.write( "1. ~N ⊃ [(B ⊃ D) ⊃ (N v ~E)]\r<BR>\n" );
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document.write( "2. (B ⊃ E) ⊃ ~N\r<BR>\n" );
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document.write( "3. B ⊃ D\r<BR>\n" );
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document.write( "4. D ⊃ E /~D\r<BR>\n" );
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document.write( "5. ~E 1,3, MD\r<BR>\n" );
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document.write( "N v ~ E 2,5 Add\r<BR>\n" );
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document.write( "57.\r<BR>\n" );
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document.write( "1. G ⊃ [~O ⊃ (G ⊃ D)]\r<BR>\n" );
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document.write( "2. O v G\r<BR>\n" );
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document.write( "3. ~O /D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826292 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Please only post one problem at a time.\r<BR>\n" );
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document.write( "I'll do problem 55 to get you started. <BR>\n" );
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document.write( "<tr><TD >Number</TD><TD >Statement</TD><TD >Line(s) Used</TD><TD >Reason</TD></tr><tr><TD >1</TD><TD >(L = N) -> C</TD><TD ></TD><TD ></TD></tr><tr><TD >2</TD><TD >(L = N) v (P -> ~E)</TD><TD ></TD><TD ></TD></tr><tr><TD >3</TD><TD >~E -> C</TD><TD ></TD><TD ></TD></tr><tr><TD >4</TD><TD >~C</TD><TD ></TD><TD ></TD></tr><tr><TD >:.</TD><TD >~P</TD><TD ></TD><TD ></TD></tr><tr><TD >5</TD><TD >~~E</TD><TD >3, 4</TD><TD >Modus Tollens</TD></tr><tr><TD >6</TD><TD >~(L = N)</TD><TD >1, 4</TD><TD >Modus Tollens</TD></tr><tr><TD >7</TD><TD >P -> ~E</TD><TD >2, 6</TD><TD >Disjunctive Syllogism</TD></tr><tr><TD >8</TD><TD >~P</TD><TD >7, 5</TD><TD >Modus Tollens</TD></tr>\n" );
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document.write( "I used a standard equal sign in place of a triple equal sign. I used arrows in place of the horseshoe symbols.\r<BR>\n" );
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document.write( "For more information, check out the various rules of inference and rules of replacement as shown in the link below.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://logiccurriculum.com/2019/02/09/rules-for-proofs/\">https://logiccurriculum.com/2019/02/09/rules-for-proofs/</a><BR>\n" );
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document.write( " </SPAN>\n" );
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