document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=337060>Question 337060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For all numbers x and y, let the operation * be defined by x * y = x - y. If a and b are positive integers, which of the following can be equal to zero?<BR>\n" );
document.write( "I. a * b <BR>\n" );
document.write( "II. (a + b) * b <BR>\n" );
document.write( "III. a * (a + b)\r<BR>\n" );
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document.write( "(A) I only <BR>\n" );
document.write( "(B) II only <BR>\n" );
document.write( "(C) III only <BR>\n" );
document.write( "(D) I and II <BR>\n" );
document.write( "(E) I and III\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #241663 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=241663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since x * y = x-y, this means that a*b = a-b. So if a=b, then a*b=a-b=a-a=0. So (I) is true.\r<BR>\n" );
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document.write( "So because x * y = x-y, we can also say that (a+b)*b = (a+b)-b = a. But if 'a' is a is a positive integer, then 'a' is NOT zero. So (II) is NOT true.\r<BR>\n" );
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document.write( "In a similar (but slightly different) fashion, (III) is also false using the same reasoning above.\r<BR>\n" );
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document.write( "So only (I) is true. \r<BR>\n" );
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document.write( "So the answer is A)\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">website</a>. \r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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