document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=627978>Question 627978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Fill in the heading of the following truth table using any of p, q, ~, , ?, , and . Use keyboard shortcuts of --> for , <--> for ?, V for , and ^ for .\r<BR>\n" );
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document.write( "p     q<BR>\n" );
document.write( "T     T      F<BR>\n" );
document.write( "T     F      F<BR>\n" );
document.write( "F     T      F<BR>\n" );
document.write( "F     F      T </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #396158 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=396158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Notice how the truth table for p ^ q has a last column of T, F, F, F\r<BR>\n" );
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document.write( "Flip everything to get F, F, F, T, which is exactly the last column in the given table above. \r<BR>\n" );
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document.write( "So we go from p ^ q to ~(p ^ q)\r<BR>\n" );
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document.write( "Now use De Morgan's Law to simplify...\r<BR>\n" );
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document.write( "~(p ^ q)\r<BR>\n" );
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document.write( "<font color=\"red\">~p V ~q</font>\r<BR>\n" );
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document.write( "So the full table is...\r<BR>\n" );
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document.write( "<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 ><font color=\"red\">~p V ~q</font></TD>\r\n" );
document.write( "</TR>\r\n" );
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document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >T</TD>\r\n" );
document.write( "  <TD >F</TD>\r\n" );
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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( "</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 >F</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( "</TR>\r\n" );
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document.write( "</TABLE>\r<BR>\n" );
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document.write( "<font color=\"red\">--------------------------------------------------------------------------------------------------------------</font><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );