document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980746>Question 980746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rues of implication<BR>\n" );
document.write( "I have been stuck on this for a while please help\r<BR>\n" );
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document.write( "~HvF<BR>\n" );
document.write( "V&~K<BR>\n" );
document.write( "I>A<BR>\n" );
document.write( "~H>I<BR>\n" );
document.write( "(VvN)>(F>~G)<BR>\n" );
document.write( "/Av~G </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601888 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You need to do a conditional proof.  The first step is to note that you can deduce V from V & ~K by simplification.  Then by Addition (or Disjunction Introduction if you prefer), you can deduce V v N.  Then by Modus Ponens we conclude F -> ~G.\r<BR>\n" );
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document.write( "Now the conditional part.  Assume G.  Then by Modus Tollens you have ~F.  ~F and ~H v F gives us ~H.  Then by Modus Ponens, ~H -> I gives us I, then by Modus Ponens again, I -> A gives us A.  In summary, assuming G we get A and from A we can conclude A v ~G by Addition.\r<BR>\n" );
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document.write( "The alternative is ~G, from which we can conclude A v ~G by addition.\r<BR>\n" );
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document.write( "Either way, A v ~G. \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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