document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=568976>Question 568976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construct a truth table for (p ^ q) -> ~q Be sure to include all intermediate steps on your table.\r<BR>\n" );
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document.write( "Because this has no assigned statements to it, I am confused as to how I would solve this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367186 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=367186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you create a truth table that includes columns for:<BR>\n" );
document.write( "p<BR>\n" );
document.write( "q<BR>\n" );
document.write( "~q<BR>\n" );
document.write( "(p ^ q)<BR>\n" );
document.write( "(p ^ q) -> ~q<BR>\n" );
document.write( "your table would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2012/feb071.jpg\" alt = \"$$$$\" /><BR>\n" );
document.write( "your table needs 2 rows per variable.<BR>\n" );
document.write( "the number of rows in your table is equal to 2 raised to the power of the number of variables.<BR>\n" );
document.write( "in this case the number of rows is 2^2 = 4<BR>\n" );
document.write( "if 3 variables, the number of rows is 2^3 = 8<BR>\n" );
document.write( "if 4 variables, the number of rows is 2^4 = 16<BR>\n" );
document.write( "this is required to capture all of the possible combinations for all of the variables in combination.<BR>\n" );
document.write( "your table only requires 2 rows because you only have 2 variables.<BR>\n" );
document.write( "they are p and q.<BR>\n" );
document.write( "the possible combinations for p and q are:<BR>\n" );
document.write( "TT, TF, FT, FF<BR>\n" );
document.write( "if you have 3 variables, then the total combinations would be 8 as shown here:<BR>\n" );
document.write( "TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF<BR>\n" );
document.write( "you only have 2 variables so we have 4 rows only as shown in the table.<BR>\n" );
document.write( "~q is the revere of q.<BR>\n" );
document.write( "when q is true, ~q is false.<BR>\n" );
document.write( "when q is false, ~q is true.<BR>\n" );
document.write( "this can be seen in the table.<BR>\n" );
document.write( "(p ^ q) is true if both p and q are true, otherwise it is false.<BR>\n" );
document.write( "this is also shown in the table.<BR>\n" );
document.write( "the only time (p ^ q) is true is when p is true and q is true.<BR>\n" );
document.write( "(p ^ q) -> ~q is only false if (p ^ q) is true and ~q is false.<BR>\n" );
document.write( "otherwise it is true.<BR>\n" );
document.write( "this can also be shown in the table.<BR>\n" );
document.write( " </SPAN>\n" );
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