document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169634>Question 1169634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this :<BR>\n" );
document.write( "A union B = A intersection B implique A = B </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794431 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1) &nbsp;&nbsp;First, &nbsp;I will prove that every element &nbsp;\"x\" &nbsp;which belongs to set &nbsp;A, &nbsp;belongs to set &nbsp;B, &nbsp;too.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2) &nbsp;&nbsp;Next, &nbsp;I will prove that every element &nbsp;\"y\" &nbsp;which belongs to set &nbsp;B, &nbsp;belongs to set &nbsp;A, &nbsp;too.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It will mean that the sets &nbsp;A &nbsp;and &nbsp;B &nbsp;are identical.\r<BR>\n" );
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document.write( "    Indeed, let x belongs to A.\r\n" );
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document.write( "    Then it belongs to (A union B).\r\n" );
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document.write( "    Due to condition, it implies that x belongs to (A intersection B).\r\n" );
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document.write( "    In turn, it means that x belongs to B.\r\n" );
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document.write( "    First statement is proved.\r\n" );
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document.write( "Now I prove the second statement (the proof is the same due to symmetry)\r<BR>\n" );
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document.write( "    Let y belongs to B.\r\n" );
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document.write( "    Then y belongs to (A union B).\r\n" );
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document.write( "    Due to condition, it implies that y belongs to (A intersection B).\r\n" );
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document.write( "    In turn, it means that y belongs to A.\r\n" );
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document.write( "    Second statement is proved.\r\n" );
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document.write( "With two statements proven, &nbsp;the posed problem is solved.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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