document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082970>Question 1082970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how can i differenciate proper and improper subsets  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696964 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=696964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a proper subset is completely contained in its superset but is not equal to its superset.\r<BR>\n" );
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document.write( "eample:\r<BR>\n" );
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document.write( "set A = {1,2,3,4,5}\r<BR>\n" );
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document.write( "set B = {1,2,3,4,5}\r<BR>\n" );
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document.write( "set C = {1,2,3,4}\r<BR>\n" );
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document.write( "set B is an improper subset of set A because it is wholly contained within set A but is also the same as set A.\r<BR>\n" );
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document.write( "set C is a proper subset of A because it is wholly contained within set A but is not also the same as set A.\r<BR>\n" );
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document.write( "every set is an improper subset of itself.\r<BR>\n" );
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document.write( "no set can ever be a proper subset of itself.\r<BR>\n" );
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document.write( "here's a definition from the web.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathcaptain.com/algebra/improper-subset.html\" target = \"_blank\">http://www.mathcaptain.com/algebra/improper-subset.html</a>\r<BR>\n" );
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document.write( "any questions, send me an email.\r<BR>\n" );
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document.write( "if a set has only 1 element, then the only proper subset is the null set.\r<BR>\n" );
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document.write( "if a set has no elements, then there is no proper subset, but there is an improper subset, namely another set that has no elements. </SPAN>\n" );
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