document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=519282>Question 519282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construct a truth table for q^ ~p  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #345512 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20059)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=345512\">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( "Construct a truth table for q ^ ~p\r\n" );
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document.write( "I'll walk yoiu through it.  Pay attention:\r\n" );
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document.write( "You begin with this:\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "Case 1\r\n" );
document.write( "Case 2\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "There are four cases \r\n" );
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document.write( "Case 1:  p has truth value T,  q has truth value T\r\n" );
document.write( "Case 2:  p  \"    \"     \"   T,  q  \"    \"     \"   F\r\n" );
document.write( "Case 3:  p  \"    \"     \"   F,  q  \"    \"     \"   T\r\n" );
document.write( "Case 4:  p  \"    \"     \"   F,  q  \"    \"     \"   F\r\n" );
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document.write( "Every time I complete a case I will color it red:\r\n" );
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document.write( "For case 1, temporarily replace the 3 p's with T's and the 2 q's with T's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "Case 1   T   T   ~T   T ^ ~T\r\n" );
document.write( "Case 2\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "Then erase the 2 ~T's and replace them by F's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "Case 1   T   T    F   T ^  F\r\n" );
document.write( "Case 2\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "Now use the rule for ^ which says we replace T ^ T by T and anything else by F\r\n" );
document.write( "So we erase the T ^ F and replace it by F\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "Case 1   T   T    F     F\r\n" );
document.write( "Case 2\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "and we are done with Case 1, so we color it red.\r\n" );
document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F</font>\r\n" );
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document.write( "---------------------------------\r\n" );
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document.write( "For case 2,  temporarily replace the 3 p's with T's and the 2 q's with F's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F</font>\r\n" );
document.write( "Case 2   T   F   ~T   F ^ ~T\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "Then erase the 2 ~T's and replace them by F's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F</font>\r\n" );
document.write( "Case 2   T   F    F   F ^  F\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "Now use the rule for ^ which says we replace T ^ T by T and anything else by F\r\n" );
document.write( "So we erase the F ^ F and replace it by F\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F</font>\r\n" );
document.write( "Case 2   T   F    F     F\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "and we are done with Case 2, so we color it red.\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F</font>\r\n" );
document.write( "Case 3\r\n" );
document.write( "Case 4\r\n" );
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document.write( "---------------------------------\r\n" );
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document.write( "For case 3, temporarily replace the 3 p's with F's and the 2 q's with T's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F</font>\r\n" );
document.write( "Case 3   F   T   ~F   T ^ ~F\r\n" );
document.write( "Case 4\r\n" );
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document.write( "Then erase the 2 ~F's and replace them by T's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F</font>\r\n" );
document.write( "Case 3   F   T    T   T ^ T\r\n" );
document.write( "Case 4\r\n" );
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document.write( "Now use the rule for ^ which says we replace T ^ T by T and anything else by F\r\n" );
document.write( "So we erase the T ^ T and replace it by T\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F</font>\r\n" );
document.write( "Case 3   F   T    T     T\r\n" );
document.write( "Case 4\r\n" );
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document.write( "and we are done with Case 3, so we color it red.\r\n" );
document.write( "\r\n" );
document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F\r\n" );
document.write( "Case 3   F   T    T     T</font>\r\n" );
document.write( "Case 4\r\n" );
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document.write( "---------------------------------\r\n" );
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document.write( "For case 4, temporarily replace the 3 p's with F's and the 2 q's with T's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F\r\n" );
document.write( "Case 3   F   T    T     T</font>\r\n" );
document.write( "Case 4   F   F   ~F   F ^ ~F \r\n" );
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document.write( "Then erase the 2 ~F's and replace them by T's\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F\r\n" );
document.write( "Case 3   F   T    T     T</font>\r\n" );
document.write( "Case 4   F   F    T   F ^ T\r\n" );
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document.write( "Now use the rule for ^ which says we replace T ^ T by T and anything else by F\r\n" );
document.write( "So we erase the F ^ T and replace it by F\r\n" );
document.write( "\r\n" );
document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F    F     F\r\n" );
document.write( "Case 3   F   T    T     T</font>\r\n" );
document.write( "Case 4   F   F    T     F\r\n" );
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document.write( "and we are done with Case 4, so we color it red.\r\n" );
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document.write( "         p   q   ~p   q ^ ~p\r\n" );
document.write( "<font color=\"red\">Case 1   T   T    F     F\r\n" );
document.write( "Case 2   T   F   ~T     F\r\n" );
document.write( "Case 3   F   T    T     T\r\n" );
document.write( "Case 4   F   F    T     F</font>\r\n" );
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document.write( "And we're done with the whole truth tablw.  You can learn to do \r\n" );
document.write( "these case by case without erasing anything, by doing those steps \r\n" );
document.write( "in your head.  It isn't hard.\r\n" );
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document.write( "Edwin</PRE>  </SPAN>\n" );
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