document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191720>Question 1191720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a set S = ℝ, prove that a relation R on S where (a , b) ∈ R and a - b = 0 is an equivalence relation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823984 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "An equivalence relation is a relation that is Reflexive, Symmetric, and Transitive:\r<BR>\n" );
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document.write( "Reflexive: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \forall (a,a)\ \in\ R\ on\ S, a\ -\ a\ =\ 0\"> therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large R\"> is reflexive.\r<BR>\n" );
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document.write( "Symmetric: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \forall (a,b)\ \in\ R\ on\ S, a\ -\ b\ =\ 0\ \right\ b\ -\ a\ =\ 0\"> therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large R\"> is symmetric.\r<BR>\n" );
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document.write( "Transitive: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \forall (a,b)\ &\ (b,c)\ \in\ R\ on\ S, \(a\ -\ b\ =\ 0\ \right\ a\ =\ b\ &\ b\ -\ c\ \right\ b\ =\ c)\ \right\ a\ =\ c\ \right\ a\ -\ c\ =\ 0\"> therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large R\"> is transitive.\r<BR>\n" );
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document.write( "R is reflexive, symmetric, and transitive, therefore R is an equivalence relation.\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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