document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=260642>Question 260642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "Can someone please help me I have asked several question but I have not received any answer, if someone would please help me with the following.\r<BR>\n" );
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document.write( "a.r: The apartment is hot. q: The air conditioner is working. p: The temperature is 90.\r<BR>\n" );
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document.write( "Write the following in symbolic form\r<BR>\n" );
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document.write( "The temperature is not 90 and the air conditioner is working, but the apartment is hot.\r<BR>\n" );
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document.write( "COnstruct a truth table for the statement\r<BR>\n" );
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document.write( "~ (~ p<---> q)<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 #192087 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=192087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "Let \r<BR>\n" );
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document.write( "r: The apartment is hot. <BR>\n" );
document.write( "q: The air conditioner is working. <BR>\n" );
document.write( "p: The temperature is 90.\r<BR>\n" );
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document.write( "By convention, the tilde symbol ~ is to denote the opposite of a given statement. So ~p denotes \"not p\" and it is the opposite of p. So if r: The apartment is hot, then ~r: the apartment is NOT hot. See the difference? \r<BR>\n" );
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document.write( "So to translate \"the temperature is not 90\", simply start with p and negate it to get ~p. To add on \"the air conditioner is working\", just combine ~p with q along with the symbol <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \wedge\"> like so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim p \wedge q\">\r<BR>\n" );
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document.write( "Remember that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \wedge\"> means \"and\"\r<BR>\n" );
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document.write( "Finally to add on \"but the apartment is hot\", just add on an additional <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \wedge\"> and r to get the final answer of \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\sim p \wedge q\right) \wedge r\">\r<BR>\n" );
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document.write( "Take note of the parenthesis. They are for grouping purposes.\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "First, start with a blank table with headers of p, q, ~p, ~p <-> q, ~(~p <-> q)\r<BR>\n" );
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document.write( "<TABLE  border=\"1\">\n" );
document.write( "<th>p</th><th>q</th><th>~p</th><th>~p <-> q</th><th>~(~p <-> q)</th><tr><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD></tr><tr><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD></tr><tr><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD></tr><tr><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD >&nbsp;</TD><TD ></TD></tr>\n" );
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document.write( "Now fill in the values T, T, F, F for the first column p and the values T, F, T, F for the second column q. This will list all of the possible combos of p and q\r<BR>\n" );
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document.write( "<th>p</th><th>q</th><th>~p</th><th>~p <-> q</th><th>~(~p <-> q)</th><tr><TD >T</TD><TD >T</TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >T</TD><TD >F</TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >F</TD><TD >T</TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >F</TD><TD >F</TD><TD ></TD><TD ></TD><TD ></TD></tr>\r\n" );
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document.write( "Negate the first column p to get the third column ~p. In other words, change each T to F (or vice versa) to get the third column ~p\r<BR>\n" );
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document.write( "<th>p</th><th>q</th><th>~p</th><th>~p <-> q</th><th>~(~p <-> q)</th><tr><TD >T</TD><TD >T</TD><TD >F</TD><TD ></TD><TD ></TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD><TD ></TD><TD ></TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD><TD ></TD><TD ></TD></tr><tr><TD >F</TD><TD >F</TD><TD >T</TD><TD ></TD><TD ></TD></tr>\r\n" );
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document.write( "Recall that p <-> q is only true when p and q have the same truth values (ie when they are equivalent). Use this fact to fill in the 4th column.\r<BR>\n" );
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document.write( "<th>p</th><th>q</th><th>~p</th><th>~p <-> q</th><th>~(~p <-> q)</th><tr><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD ></TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD ></TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD ></TD></tr><tr><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD ></TD></tr>\n" );
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document.write( "Finally, negate the 4th column to get the fifth and final column.\r<BR>\n" );
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document.write( "<th>p</th><th>q</th><th>~p</th><th>~p <-> q</th><th>~(~p <-> q)</th><tr><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >F</TD></tr><tr><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD >T</TD></tr>\n" );
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