document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185765>Question 185765</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/032150108X/algebrahomeworkh>A Survey of Mathematics with Application</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am actually getting myself confused here: Please Help!\r<BR>\n" );
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document.write( "a.) If today is Monday, then tomorrow is not Wednesday.\r<BR>\n" );
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document.write( "b.) If it is false that today is Monday and tomorrow is not Wednesday\r<BR>\n" );
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document.write( "c.) Today is not Monday or tomorrow is Wednesday.\r<BR>\n" );
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document.write( "I personally would say that A & B are equivalent, but the more I read over it and convince myself that A & B are equivalent, the more I confuse myself.  Can you please help me determine which statements are equivalent.  Thanks A million everyone<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139314 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=139314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let P = today is Monday and Q = today is Wednesday\r<BR>\n" );
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document.write( "Now translate: \r<BR>\n" );
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document.write( "a) \"If today is Monday, then tomorrow is not Wednesday\" translates to \"If P then Q\" which symbolically looks like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P \Rightarrow \sim Q\">\r<BR>\n" );
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document.write( "Now fill out a truth table:\r<BR>\n" );
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document.write( "<tr><TD >P</TD><TD >Q</TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim Q\"></TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P \Rightarrow \sim Q\"></TD></tr>\r\n" );
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document.write( "<tr><TD >T</TD><TD >T</TD><TD >F</TD><TD ><font color=\"red\">F</font></TD></tr>\r\n" );
document.write( "<tr><TD >T</TD><TD >F</TD><TD >T</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >T</TD><TD >F</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >F</TD><TD >T</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
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document.write( "Note: let me know if you need help constructing a truth table\r<BR>\n" );
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document.write( "The truth values in red are the values we're going to compare later.\r<BR>\n" );
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document.write( "b) \"If it is false that today is Monday and tomorrow is not Wednesday\" translates to \"It is NOT the case that P and not Q are true\".\r<BR>\n" );
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document.write( "In symbolic form, the expression looks like: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim\left(P \wedge \sim Q\right)\">\r<BR>\n" );
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document.write( "Now fill out a truth table:\r<BR>\n" );
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document.write( "<tr><TD >P</TD><TD >Q</TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim Q\"></TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P \wedge \sim Q\"></TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim\left(P \wedge \sim Q\right)\"><BR>\n" );
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document.write( "<tr><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
document.write( "<tr><TD >T</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD ><font color=\"red\">F</font></TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
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document.write( "c) \r<BR>\n" );
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document.write( "\"Today is not Monday or tomorrow is Wednesday\" translates to \"Not P or Q\" which looks like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim P \vee Q\">\r<BR>\n" );
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document.write( "Now make a truth table\r<BR>\n" );
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document.write( "<tr><TD >P</TD><TD >Q</TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim P\"></TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim P \vee Q\"></TD>\r\n" );
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document.write( "<tr><TD >T</TD><TD >T</TD><TD >F</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
document.write( "<tr><TD >T</TD><TD >F</TD><TD >F</TD><TD ><font color=\"red\">F</font></TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >T</TD><TD >T</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >F</TD><TD >T</TD><TD ><font color=\"red\">T</font></TD></tr>\r\n" );
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document.write( "</TABLE>\r<BR>\n" );
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document.write( "Now comparing the truth values that are marked in red from parts a) to c), we see that the red truth values in tables b) and c) are identical. So this means that statements b) and c) are equivalent.<BR>\n" );
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