document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036260>Question 1036260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the properties of operations/ relations being illustrated:<BR>\n" );
document.write( "a) 	3&#8729;(x&#8729;5)=(x&#8729;5)&#8729;3<BR>\n" );
document.write( "b)	(a+b)+0=a+b<BR>\n" );
document.write( "c)	If a is a real number, then a + 8 is a real number<BR>\n" );
document.write( "d)	If a + b = c – d and c – d = e, then a + b = e.<BR>\n" );
document.write( "e)	&#8730;3+(-&#8730;3)=0 <BR>\n" );
document.write( "f)	(a+b)&#8729;(x-y)=a&#8729;(x-y)+b&#8729;(x-y)<BR>\n" );
document.write( "g)	(x+5)&#8729;(y-3)=(y-3)&#8729;(x+5)<BR>\n" );
document.write( "h)	(2r+3s)+4t=2r+(3s+4t)<BR>\n" );
document.write( "i)	5=5<BR>\n" );
document.write( "j)	If a + 4 = b – 1, then b – 1 = a + 4.\r<BR>\n" );
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document.write( "Operations: Closure, Commutativity, associativity, identity, inverse<BR>\n" );
document.write( "Relations: transitive, reflexive, symmetric<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650919 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=650919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) 	3&#8729;(x&#8729;5)=(x&#8729;5)&#8729;3 --->Commutativity<BR>\n" );
document.write( "b)	(a+b)+0=a+b --->additive identity<BR>\n" );
document.write( "c)	If a is a real number, then a + 8 is a real number ---> Closure<BR>\n" );
document.write( "d)	If a + b = c – d and c – d = e, then a + b = e. ---> Transitive<BR>\n" );
document.write( "e)	&#8730;3+(-&#8730;3)=0  ---> additive inverse<BR>\n" );
document.write( "f)	(a+b)&#8729;(x-y)=a&#8729;(x-y)+b&#8729;(x-y) ---> Distributivity<BR>\n" );
document.write( "g)	(x+5)&#8729;(y-3)=(y-3)&#8729;(x+5) ---> Commutativity<BR>\n" );
document.write( "h)	(2r+3s)+4t=2r+(3s+4t) ---> Associativity<BR>\n" );
document.write( "i)	5=5 ---> Reflexive<BR>\n" );
document.write( "j)	If a + 4 = b – 1, then b – 1 = a + 4. --> Symmetric\r<BR>\n" );
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document.write( "Operations: Closure, Commutativity, associativity, identity, inverse<BR>\n" );
document.write( "Relations: transitive, reflexive, symmetric<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );