document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174925>Question 174925</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1567655157/algebrahomeworkh>Integrated Mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Present a formal proof in logic, using the laws of inference to reace the conclusion.\r<BR>\n" );
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document.write( "P-->A<BR>\n" );
document.write( "G-->~R<BR>\n" );
document.write( "A-->R<BR>\n" );
document.write( "G v H<BR>\n" );
document.write( "P<BR>\n" );
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document.write( "Therefore : H </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130325 by </B><A HREF=/tutors/aboutme.mpl?userid=EMStelley><B>EMStelley(208)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EMStelley><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=EMStelley><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This may not be the most eloquent proof, and I'm sure there are many others, but here is one version that works:\r<BR>\n" );
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document.write( "Since G -> ~R we have that R -> ~G.<BR>\n" );
document.write( "Since P -> A and A -> R and R -> ~G, we have P -> ~G.  Since G V H and P is true, then H must be true.  (Not G is true, so to make G V H true, H must be true).  Hope this helps! </SPAN>\n" );
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