document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=843102>Question 843102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If p    q  is true and q  is true, then p  is neveralwayssometimes tr </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #507937 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=507937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the symbol you were trying to show didn't show up.\r<BR>\n" );
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document.write( "the following truth table should give you your answer, since it covers all the most common symbols that you may have meant.\r<BR>\n" );
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document.write( "p         q         p v q      p ^ q     p ---> q      p <---> q\r\n" );
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document.write( "T         T           T          T          T              T\r\n" );
document.write( "T         F           T          F          F              F\r\n" );
document.write( "F         T           T          F          T              F\r\n" );
document.write( "F         F           F          F          T              T\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "the first 2 columns are p and q individual states (either true or false)<BR>\n" );
document.write( "the third column is p or q, with the v symbolizing or.<BR>\n" );
document.write( "the fourth column is p and q, with the ^ symbolizing and.<BR>\n" );
document.write( "the fifth column is p implies q, with the ---> symbolizing implies.<BR>\n" );
document.write( "the sixth column is q if and only if p, with the <---> symbolizing if and only if.\r<BR>\n" );
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document.write( "the question was:\r<BR>\n" );
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document.write( "If p    q  is true and q  is true, then p  is never/always/sometimes true\r<BR>\n" );
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document.write( "If or is indicated (v), then the answer is sometimes, because the or condition only requires that one of them be true.\r<BR>\n" );
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document.write( "If and is indicated (^), then the answer is always, because the and condition requires both of them to be true.\r<BR>\n" );
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document.write( "if implies is indicated (--->), then the answer is sometimes because the implies condition allows q to be true regardless of whether p is true or false.\r<BR>\n" );
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document.write( "if if and only if is indicated (<--->), then the answer is always because the if and only condition requires both to be true.\r<BR>\n" );
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document.write( "In the truth table, if you only look at the lines where Q is true, you may be able to spot this better.\r<BR>\n" );
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document.write( "Only those lines are duplicated  below:\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( "p         q         p v q      p ^ q     p ---> q      p <---> q\r\n" );
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document.write( "T         T           T          T          T              T\r\n" );
document.write( "F         T           T          F          T              F\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "you can see on the first line, that p is true and this allows all other conditions to be true.\r<BR>\n" );
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document.write( "on the second line p is false.<BR>\n" );
document.write( "the or condition is still true and the implies condition is still true.<BR>\n" );
document.write( "the and condition and the if and only if condition, require p to also be true so they are false.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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