document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835126>Question 835126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that if a set is an improper subset of another set, then the two set are equal </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503400 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=503400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X and Y be two sets. Let X be a subset of Y. So everything in X is also found in Y. \r<BR>\n" );
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document.write( "If X is a subset then the only two things are possible: it is a proper subset or it is an improper subset. \r<BR>\n" );
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document.write( "If it is a proper subset, then X will have less than Y (since X will be smaller). \r<BR>\n" );
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document.write( "If X is an improper subset, then X will have the same number of items in set Y. This will force X to be equal to Y. \r<BR>\n" );
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document.write( "If the two weren't equal for instance, then Y would have some element that is not in X, but that would make Y larger and hence X would be a proper subset. \r<BR>\n" );
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document.write( "However, X is an improper subset, which would again force Y to not have that extra element. So this proves that X = Y. </SPAN>\n" );
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