document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856511>Question 856511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let * denote the binary operation defined on Q, the set of all rational numbers, by x*y=3xy, for all x, y in Q. Exactly which of the following properties does * have?<BR>\n" );
document.write( "i. Commutativity <BR>\n" );
document.write( "ii. Associativity<BR>\n" );
document.write( "iii. Has an identity </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515982 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=515982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Commutative:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay=3xy ALIGN=MIDDLE  ALT=\"x%2Ay=3xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Ax=3yx=3xy ALIGN=MIDDLE  ALT=\"y%2Ax=3yx=3xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay=y%2Ax ALIGN=MIDDLE  ALT=\"x%2Ay=y%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "It is commutative.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ay%29%2Az=3%28x%2Ay%29z=3%283xy%29%29z=9xyz ALIGN=MIDDLE  ALT=\"%28x%2Ay%29%2Az=3%28x%2Ay%29z=3%283xy%29%29z=9xyz\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%28y%2Az%29=3x%28y%2Az%29=3x%283yz%29=9xyz ALIGN=MIDDLE  ALT=\"x%2A%28y%2Az%29=3x%28y%2Az%29=3x%283yz%29=9xyz\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ay%29%2Az=x%2A%28y%2Az%29 ALIGN=MIDDLE  ALT=\"%28x%2Ay%29%2Az=x%2A%28y%2Az%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It is associative.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "What exactly do you mean by identity for a two input operation?<BR>\n" );
document.write( "Do you want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay=1 ALIGN=MIDDLE  ALT=\"x%2Ay=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >???<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );