document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=474977>Question 474977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Let p represent the statement, \"Jim plays football\", and let q represent \"Michael plays basketball\". Convert the compound statements into symbols.\r<BR>\n" );
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document.write( "It is not the case that Jim plays football and Michael does not play basketball.<BR>\n" );
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document.write( "       ~p  q <BR>\n" );
document.write( "       ~p  ~q <BR>\n" );
document.write( "       ~(p  q) <BR>\n" );
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 #325713 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=325713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >: Jim plays football<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" >: Michael plays basketball\r<BR>\n" );
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document.write( "that means is that wherever you see a '<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >', it will stand for \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Jim ALIGN=MIDDLE  ALT=\"Jim\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=plays ALIGN=MIDDLE  ALT=\"plays\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+football ALIGN=MIDDLE  ALT=\"+football\"   DISABLED_style= \"max-width:90%; height:auto;\" >\". \r<BR>\n" );
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document.write( "The symbol ~ stands for the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negation ALIGN=MIDDLE  ALT=\"negation\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a given statement. So ~<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p ALIGN=MIDDLE  ALT=\"+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( " So if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > means \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Jim ALIGN=MIDDLE  ALT=\"Jim\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=plays ALIGN=MIDDLE  ALT=\"plays\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+football ALIGN=MIDDLE  ALT=\"+football\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", then ~p: \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Jim ALIGN=MIDDLE  ALT=\"Jim\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=plays ALIGN=MIDDLE  ALT=\"plays\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+football ALIGN=MIDDLE  ALT=\"+football\"   DISABLED_style= \"max-width:90%; height:auto;\" >\". \r<BR>\n" );
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document.write( "Also, the symbol <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > stands for \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=or ALIGN=MIDDLE  ALT=\"or\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"\r<BR>\n" );
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document.write( "First, take a look at the statement \"Jim does not play football or Michael plays basketball\". We are going to ignore the beginning part \"It is not the case\" for now.\r<BR>\n" );
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document.write( "So \"Jim does not play football\" translates to  ~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > and \"Michael plays basketball\" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Combine the two symbols with a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get ~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since we're dealing with an 'or' situation)\r<BR>\n" );
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document.write( "Finally, negate the entire statement by placing a <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim\"> outside the parenthesis to get ~(~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" >), because the beginning of the sentence states that \"it is not the case\". \r<BR>\n" );
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document.write( "So the full translation of \"It is not the case that Jim does not play football or Michael plays basketball\" is ~(~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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