document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=613312>Question 613312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a formal proof of validity for the given arguments<BR>\n" );
document.write( "A)<BR>\n" );
document.write( "1. (R>S)<BR>\n" );
document.write( "2. V v~S<BR>\n" );
document.write( "3. ~V/.'.~R<BR>\n" );
document.write( "B)<BR>\n" );
document.write( "1. W.(XvY)<BR>\n" );
document.write( "2. W<BR>\n" );
document.write( "3. ~X/.'.YvZ<BR>\n" );
document.write( "C)<BR>\n" );
document.write( "1. A * ~ B / .'. B > C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385952 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=385952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "1. (R>S)\r\n" );
document.write( "2. V v~S\r\n" );
document.write( "3. ~V/.'.~R\r\n" );
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document.write( "4. ~S            2,3   Disjunctive syllogism\r\n" );
document.write( "5. ~R            1,4   Modus Tollens\r\n" );
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document.write( "B)\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "1. W.(XvY)\r\n" );
document.write( "2. W\r\n" );
document.write( "3. ~X/.'.YvZ\r\n" );
document.write( "---------------\r\n" );
document.write( "4. (X v Y).W      1     Commutation\r\n" );
document.write( "5. X v Y          4     Simplification\r\n" );
document.write( "6. Y v X          5     Commutation\r\n" );
document.write( "7. Y              6,3   Disjunctive syllogism\r\n" );
document.write( "8. Y v Z          7     Addition\r\n" );
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document.write( "C)\r<BR>\n" );
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document.write( "1. A * ~ B / .'. B > C\r\n" );
document.write( "---------------------\r\n" );
document.write( "2. ~B * A           1    Commutation\r\n" );
document.write( "3. ~B               2    Simplification\r\n" );
document.write( "4. ~B v C           3    Addition\r\n" );
document.write( "5. B > C            4    Material Implication\r\n" );
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document.write( " </SPAN>\n" );
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