document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009274>Question 1009274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve this proof? I am stuck at line six. \r<BR>\n" );
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document.write( "1.   (A &#8594; E) &#8594; (D &#8744; C)            <BR>\n" );
document.write( "2.   D &#8594; (~B &#8594; C)                 &#8756; ~C &#8594; (A &#8744; B)\r<BR>\n" );
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document.write( "|3.  ~C                       Assume<BR>\n" );
document.write( "||4. ~A                       Assume<BR>\n" );
document.write( "||5. (D&#8729;~B)&#8594;C                2, EX<BR>\n" );
document.write( "||6.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #624862 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=624862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The idea is to assume ~C is true (line 3). Using the <a  rel=nofollow HREF= \"https://www.blinn.edu/brazos/humanities/avoelkel/logic%20note%20sheet.pdf\">rules of inference/replacement</a>, if we can lead to A v B somehow (line 25), then that proves ~C -> (A v B) 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 -&gt; E) -&gt; (D v C)</TD><TD ></TD><TD ></TD></tr><tr><TD >2</TD><TD ></TD><TD >D -&gt; (~B -&gt; C)</TD><TD ></TD><TD ></TD></tr><tr><TD >:.</TD><TD ></TD><TD >~C -&gt; (A v B)</TD><TD ></TD><TD ></TD></tr><tr><TD ></TD><TD >3</TD><TD >~C</TD><TD ></TD><TD >ACP</TD></tr><tr><TD ></TD><TD >4</TD><TD >(D &amp; ~B) -&gt; C</TD><TD >2</TD><TD >EXP</TD></tr><tr><TD ></TD><TD >5</TD><TD >~(D &amp; ~B)</TD><TD >4,3</TD><TD >MT</TD></tr><tr><TD ></TD><TD >6</TD><TD >~D v ~~B</TD><TD >5</TD><TD >DM</TD></tr><tr><TD ></TD><TD >7</TD><TD >~D v B</TD><TD >6</TD><TD >DN</TD></tr><tr><TD ></TD><TD >8</TD><TD >D -&gt; B</TD><TD >7</TD><TD >MI</TD></tr><tr><TD ></TD><TD >9</TD><TD >~B -&gt; ~D</TD><TD >8</TD><TD >Trans</TD></tr><tr><TD ></TD><TD >10</TD><TD >~(A -&gt; E) v (D v C)</TD><TD >1</TD><TD >MI</TD></tr><tr><TD ></TD><TD >11</TD><TD >~(~A v E) v (D v C)</TD><TD >10</TD><TD >MI</TD></tr><tr><TD ></TD><TD >12</TD><TD >(~~A &amp; ~E) v (D v C)</TD><TD >11</TD><TD >DM</TD></tr><tr><TD ></TD><TD >13</TD><TD >(A &amp; ~E) v (D v C)</TD><TD >12</TD><TD >DN</TD></tr><tr><TD ></TD><TD >14</TD><TD >(D v C) v (A &amp; ~E)</TD><TD >13</TD><TD >Comm</TD></tr><tr><TD ></TD><TD >15</TD><TD >[(D v C) v A] &amp; [(D v C) v ~E]</TD><TD >14</TD><TD >Dist</TD></tr><tr><TD ></TD><TD >16</TD><TD >(D v C) v A</TD><TD >15</TD><TD >Simp</TD></tr><tr><TD ></TD><TD >17</TD><TD >(C v D) v A</TD><TD >16</TD><TD >Comm</TD></tr><tr><TD ></TD><TD >18</TD><TD >C v (D v A)</TD><TD >17</TD><TD >Assoc</TD></tr><tr><TD ></TD><TD >19</TD><TD >D v A</TD><TD >18,3</TD><TD >DS</TD></tr><tr><TD ></TD><TD >20</TD><TD >~~D v A</TD><TD >19</TD><TD >DN</TD></tr><tr><TD ></TD><TD >21</TD><TD >~D -&gt; A</TD><TD >20</TD><TD >MI</TD></tr><tr><TD ></TD><TD >22</TD><TD >~B -&gt; A</TD><TD >9,21</TD><TD >HS</TD></tr><tr><TD ></TD><TD >23</TD><TD >~~B v A</TD><TD >22</TD><TD >MI</TD></tr><tr><TD ></TD><TD >24</TD><TD >B v A</TD><TD >23</TD><TD >DN</TD></tr><tr><TD ></TD><TD >25</TD><TD >A v B</TD><TD >24</TD><TD >Comm</TD></tr><tr><TD >26</TD><TD ></TD><TD >~C -&gt; (A v B)</TD><TD >3-25</TD><TD >CP</TD></tr>\n" );
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document.write( "Acroynyms/Abbreviations used\r<BR>\n" );
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document.write( "ACP = assumption for conditional proof<BR>\n" );
document.write( "Assoc = associative property<BR>\n" );
document.write( "Comm = commutation<BR>\n" );
document.write( "CP = conditional proof<BR>\n" );
document.write( "Dist = distribution<BR>\n" );
document.write( "DM = de morgan's law<BR>\n" );
document.write( "DN = double negation<BR>\n" );
document.write( "DS = disjunctive syllogism<BR>\n" );
document.write( "EXP = exportation<BR>\n" );
document.write( "HS = hypothetical syllogism<BR>\n" );
document.write( "MI = material implication<BR>\n" );
document.write( "MT = modus tollens<BR>\n" );
document.write( "Simp = simplification<BR>\n" );
document.write( "Trans = transposition </SPAN>\n" );
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