document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=588757>Question 588757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use truth tables to test the validity of the argument.\r<BR>\n" );
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document.write( "p &#8594; ~q<BR>\n" );
document.write( "q &#8594; ~p<BR>\n" );
document.write( "&#8756; p &#8744; q<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374594 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=374594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
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document.write( "<TR>\r\n" );
document.write( "  <TD >p</TD>\r\n" );
document.write( "  <TD >q</TD>\r\n" );
document.write( "  <TD >~p</TD>\r\n" );
document.write( "  <TD >~q</TD>\r\n" );
document.write( "  <TD >p -> ~q</TD>\r\n" );
document.write( "  <TD >q -> ~p</TD>\r\n" );
document.write( "  <TD >p v q</TD>\r\n" );
document.write( "</TR>\r\n" );
document.write( "<TR>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "</TR>\r\n" );
document.write( "<TR>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "</TR>\r\n" );
document.write( "<TR>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "</TR>\r\n" );
document.write( "<TR>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
document.write( "</TR>\r\n" );
document.write( "\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Notice how in the columns \"p -> ~q\" and \"q -> ~p\" the last row has T and T, but the conclusion is false. \r<BR>\n" );
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document.write( "Recall that if you have an argument with all true premises, but a false conclusion, then the argument is invalid.\r<BR>\n" );
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document.write( "So the argument is <font color=\"red\">invalid</font>. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );