document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125684>Question 1125684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Choose one of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the argument. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8.\r<BR>\n" );
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document.write( "(G • P) &#8594; K, E &#8594; Z, ~P &#8594; ~ Z, G &#8594; (E v L), therefore, (G • ~L) &#8594; K<BR>\n" );
document.write( "(S v T) &#8596; ~E, S &#8594; (F • ~G), A &#8594; W, T &#8594; ~W, therefore, (~E • A) &#8594; ~G<BR>\n" );
document.write( "(S v T) v (U v W), therefore, (U v T) v (S v W)<BR>\n" );
document.write( "~Q &#8594; (L &#8594; F), Q &#8594; ~A, F &#8594; B, L, therefore, ~A v B<BR>\n" );
document.write( "~S &#8594; (F &#8594; L), F &#8594; (L &#8594; P), therefore, ~S &#8594; (F &#8594; P)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742019 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=742019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "I'm going to pick on the first line <BR>\n" );
document.write( "(G • P) &#8594; K, E &#8594; Z, ~P &#8594; ~ Z, G &#8594; (E v L), therefore, (G • ~L) &#8594; K<BR>\n" );
document.write( "to prove that out. \r<BR>\n" );
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document.write( "I'll do so in two ways. The first of which is through a conditional proof\r<BR>\n" );
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document.write( "Start with the antecedent of the conclusion, which is (G & ~L) and show how it leads to K<BR>\n" );
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document.write( "note: I used an ampersand in place of a dot\r<BR>\n" );
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document.write( "Then I'll show how to do a proof by contradiction (aka reductio ad absurdum), which is an indirect proof. \r<BR>\n" );
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document.write( "The idea is to assume the complete opposite the conclusion, and then show how a contradiction arises.<BR>\n" );
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