document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190470>Question 1190470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT 145: Topics In Contemporary Math\r<BR>\n" );
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document.write( "QUESTION 6\r<BR>\n" );
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document.write( "Create a truth table for the following.\r<BR>\n" );
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document.write( "left parenthesis p rightwards arrow q right parenthesis logical and left parenthesis r space logical or space tilde p right parenthesis\r<BR>\n" );
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document.write( "(p --> q) ∧ (r V ~ p) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822118 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=822118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "T = true<BR>\n" );
document.write( "F = false\r<BR>\n" );
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document.write( "Here are some facts to memorize<ul><li>p v q is false when both p and q are false together; otherwise it's true</li><li>p ^ q is true when both p and q are true together; otherwise, it's false</li><li>p -> q is false when p is true and q is false; otherwise it's true</li><li>~p is the opposite of column p (i.e. flip everything in column p)</li></ul>With all that in mind, we have this truth table<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >p</TD><TD >q</TD><TD >r</TD><TD >~p</TD><TD >p -> q</TD><TD >r v ~p</TD><TD >(p -> q) ^ (r v ~p)</TD></tr><tr><TD >T</TD><TD >T</TD><TD >T</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD></tr><tr><TD >T</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >T</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr>\n" );
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document.write( "Notice we need 8 rows because of the 3 variables (p,q,r).<BR>\n" );
document.write( "2^3 = 8\r<BR>\n" );
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document.write( "Column p has four T's in a row, followed by four F's in a row.<BR>\n" );
document.write( "Column q has two copies of TTFF<BR>\n" );
document.write( "Column r has four copies of TF<BR>\n" );
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