document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009036>Question 1009036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the argument valid. Where = stands for a bi-conditional.\r<BR>\n" );
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document.write( "~(A & B) = ~C<BR>\n" );
document.write( "(D v E) > C // E > A </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #624646 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=624646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to use a conditional proof. So that means we assume E is true (line 3). If we can show it leads to A (line 12), then E > A is true.\r<BR>\n" );
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document.write( "<tr><th colspan=\"2\">Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><TD >1</TD><TD ></TD><TD >~(A &amp; B) = ~C</TD><TD ></TD><TD ></TD></tr><tr><TD >2</TD><TD ></TD><TD >(D v E) &gt; C</TD><TD ></TD><TD ></TD></tr><tr><TD >.:</TD><TD ></TD><TD >E &gt; A</TD><TD ></TD><TD ></TD></tr><tr><TD ></TD><TD >3</TD><TD >E</TD><TD ></TD><TD >ACP</TD></tr><tr><TD ></TD><TD >4</TD><TD >E v D</TD><TD >3</TD><TD >Add</TD></tr><tr><TD ></TD><TD >5</TD><TD >D v E</TD><TD >4</TD><TD >Comm</TD></tr><tr><TD ></TD><TD >6</TD><TD >C</TD><TD >2,5</TD><TD >MP</TD></tr><tr><TD ></TD><TD >7</TD><TD >~~C</TD><TD >6</TD><TD >DN</TD></tr><tr><TD ></TD><TD >8</TD><TD >[~(A &amp; B) &gt; ~C] &amp; [~C &gt; ~(A &amp; B)]</TD><TD >1</TD><TD >ME</TD></tr><tr><TD ></TD><TD >9</TD><TD >~(A &amp; B) &gt; ~C</TD><TD >8</TD><TD >Simp</TD></tr><tr><TD ></TD><TD >10</TD><TD >~~(A &amp; B)</TD><TD >9,7</TD><TD >MT</TD></tr><tr><TD ></TD><TD >11</TD><TD >A &amp; B</TD><TD >10</TD><TD >DN</TD></tr><tr><TD ></TD><TD >12</TD><TD >A</TD><TD >11</TD><TD >Simp</TD></tr><tr><TD >13</TD><TD ></TD><TD >E &gt; A</TD><TD >3-12</TD><TD >CP</TD></tr>\n" );
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document.write( "Abbreviations/Acronyms Used:\r<BR>\n" );
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document.write( "ACP = Assumption for Conditional Proof<BR>\n" );
document.write( "Add = Addition<BR>\n" );
document.write( "Comm = Commutation<BR>\n" );
document.write( "CP = Conditional Proof<BR>\n" );
document.write( "DN = Double Negation<BR>\n" );
document.write( "ME = Material Equivalence<BR>\n" );
document.write( "MP = Modus Ponens<BR>\n" );
document.write( "MT = Modus Tollens<BR>\n" );
document.write( "Simp = Simplification </SPAN>\n" );
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