document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974543>Question 974543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a.If A has six elements and B has eight elements, how many elements are in A x B?<BR>\n" );
document.write( "b. If A has g elements and B has h elements, how many elements are in A x B?<BR>\n" );
document.write( "c. If A has g elements, B has h elements, and C has k elements, how many elements are in (A x B) x C? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #596420 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=596420\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "There are 6*8 = <font color=\"red\">48</font> elements in set A x B\r<BR>\n" );
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document.write( "Rule: If there are m elements in A, n elements in B, then there are m*n elements in A x B. Draw out a table to see why this works.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "We use the same rule applied in part a). There are <font color=\"red\">g*h</font> elements in A x B. If we knew the numeric values of g and h, we can get a single numeric answer like we did in part a).\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "There are <font color=\"red\">g*h*k</font> elements in (A x B) x C\r<BR>\n" );
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document.write( "Think of A x B as one set. Call it Q. In other words, let Q = A x B\r<BR>\n" );
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document.write( "So (A x B) x C turns into Q x C and we'll use the rules applied in part a) and part b). Q is going to have g*h elements in it. So Q x C has (g*h)*k = g*h*k elements in it.\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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