document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046926>Question 1046926</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help with this?\r<BR>\n" );
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document.write( "Let &#963; be the relation on N defined by x &#963; y if and only if x &#8804; y &#8804; 2x.\r<BR>\n" );
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document.write( "Prove that &#963; is reflexive\r<BR>\n" );
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document.write( "Is &#963; transitive?\r<BR>\n" );
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document.write( "thank you very much  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662478 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=662478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) reflexive means a sigma a, then<BR>\n" );
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document.write( "x sigma x then x < or = x < or = 2x<BR>\n" );
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document.write( "note x = x and x < 2x<BR>\n" );
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document.write( "sigma is reflexive<BR>\n" );
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document.write( "b) sigma is transitive if we have<BR>\n" );
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document.write( "x sigma y and y sigma z then  x sigma z<BR>\n" );
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document.write( "we have the following <BR>\n" );
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document.write( "x sigma y then x < or = y < or = 2x<BR>\n" );
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document.write( "y sigma z then y < or = z < or = 2y<BR>\n" );
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document.write( "since < or = is an ordered relation, we know<BR>\n" );
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document.write( "x < or = z and z < or = 2y but is z < or = 2x?<BR>\n" );
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document.write( "the example is x=1, y=2, z=3<BR>\n" );
document.write( "x sigma y is 1 < or = 2 < or = 2<BR>\n" );
document.write( "y sigma z is 2 < or = 3 < or = 4<BR>\n" );
document.write( "x sigma z is 1 < or = 3 < or = 2 *** this is false<BR>\n" );
document.write( "sigma is not transitive<BR>\n" );
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