document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182111>Question 1182111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana.\r<BR>\n" );
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document.write( "Alabama	Arkansas	Louisiana<BR>\n" );
document.write( "soybeans (s)	soybeans (s)	soybeans (s) <BR>\n" );
document.write( "peanuts (p)	rice (r)	sugarcane No<BR>\n" );
document.write( "corn (c)	cotton (t)	rice (r)<BR>\n" );
document.write( "hay heart	hay heart	corn (c)<BR>\n" );
document.write( "wheat (w)	wheat (w)	cotton (t)\r<BR>\n" );
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document.write( "Let U be the smallest possible universal set that includes all of the crops listed; and let A, K, and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.\r<BR>\n" );
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document.write( "K ∪ L </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812135 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=812135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
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document.write( "<tr><TD >Alabama</TD><TD >Arkansas</TD><TD >Louisiana</TD></tr><tr><TD >soybeans (s)</TD><TD >soybeans (s)</TD><TD >soybeans (s) </TD></tr><tr><TD >peanuts (p)</TD><TD >rice (r)</TD><TD >sugarcane No</TD></tr><tr><TD >corn (c)</TD><TD >cotton (t)</TD><TD >rice (r)</TD></tr><tr><TD >hay heart</TD><TD >hay heart</TD><TD >corn (c)</TD></tr><tr><TD >wheat (w)</TD><TD >wheat (w)</TD><TD >cotton (t)</TD></tr>\n" );
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document.write( "To be honest, I'm not sure what your teacher meant by \"sugarcane no\", but I have a feeling it was supposed to be some kind of symbol. \r<BR>\n" );
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document.write( "Regardless, I'll just list the crops in word format.\r<BR>\n" );
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document.write( "K = set of crops from Arkansas<BR>\n" );
document.write( "K = {soybeans, rice, cotton, hay, wheat}<BR>\n" );
document.write( "We simply just list everything in the second column of the table above.\r<BR>\n" );
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document.write( "L = set of crops from Louisana<BR>\n" );
document.write( "L = {soybeans, sugarcane, rice, corn, cotton}<BR>\n" );
document.write( "Same idea but we look at the third column now.\r<BR>\n" );
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document.write( "The set K u L is the following<BR>\n" );
document.write( "K u L = <font color=red>{soybeans, rice, cotton, hay, wheat, sugarcane, corn}</font><BR>\n" );
document.write( "What I did was start with set K. Then I added items from set L such that I didn't repeat any crops. With any set, we simply list the item once and only once. No repeats are allowed. The order of the set doesn't matter.\r<BR>\n" );
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document.write( "The 'u' refers to \"set union\". Think of two people getting married and forming a union together. When they move in together, the bride and groom's various stuff (eg: couch, fridge, etc) will go from 2 separate houses to one house. The house represents the set while the furniture are the elements of the set. When forming a set union, we don't have repeated elements, so for example they won't have two fridges when they move in together. \r<BR>\n" );
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document.write( "Here's another example of a set union<BR>\n" );
document.write( "A = {p,q,r}<BR>\n" );
document.write( "B = {p,s,w}<BR>\n" );
document.write( "A u B = {p,q,r,   s,w}<BR>\n" );
document.write( "We don't list the item 'p' a second time.\r<BR>\n" );
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document.write( "Note: be sure not to mix up the union symbol with the universal set notation. Unfortunately both look nearly identical. \r<BR>\n" );
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document.write( "Answer: <font color=red>{soybeans, rice, cotton, hay, wheat, sugarcane, corn}</font><BR>\n" );
document.write( "Replace the words with their corresponding symbols if your teacher requires it.<BR>\n" );
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