document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=647896>Question 647896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We use the word \"and\" the symbol &#8745; (\"cap\") to get only those elements that are in one set and are in the other set.  \r<BR>\n" );
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document.write( "For the following combination of sets, perform the indicated operations: { 1, 3, 5, 7 } &#8745; { 2, 4, 6, 8 }  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406456 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406456\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> { 1, 3, 5, 7 } &#8745; { 2, 4, 6, 8 } ={} (empty set, its size or cardinality (count of elements in a set) is zero)\r<BR>\n" );
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document.write( "explanation:\r<BR>\n" );
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document.write( "The intersection is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=only ALIGN=MIDDLE  ALT=\"only\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=common ALIGN=MIDDLE  ALT=\"common\"   DISABLED_style= \"max-width:90%; height:auto;\" > elements.\r<BR>\n" );
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document.write( " To find the intersection of these two sets, we need to find out what elements they have in common. \r<BR>\n" );
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document.write( "The numbers { 1, 3, 5, 7 } are elements of one set, and { 2, 4, 6, 8 } are elements of other set. As you can see, there is no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=common ALIGN=MIDDLE  ALT=\"common\"   DISABLED_style= \"max-width:90%; height:auto;\" > elements except empty set , therefore the intersections of these two sets is {}.(empty set)\r<BR>\n" );
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document.write( "Recall, the empty set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=included ALIGN=MIDDLE  ALT=\"included\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=any ALIGN=MIDDLE  ALT=\"any\"   DISABLED_style= \"max-width:90%; height:auto;\" > set, it is also included in these sets although you don't see it.\r<BR>\n" );
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document.write( "Therefore, the empty set is the only thing set { 1, 3, 5, 7 } and set { 2, 4, 6, 8 } have in common.\r<BR>\n" );
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