document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091470>Question 1091470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to a survey, 16 people liked ham, 19 liked eggs, 18 liked mackerel, 8 liked mackerel and eggs, 5 liked ham and eggs, 7 liked ham and mackerel, and 3 liked all three foods. (is it possible to see a Venn diagram of this?)\r<BR>\n" );
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document.write( "- how many liked only mackerel?<BR>\n" );
document.write( "- how many liked at least two of three foods?<BR>\n" );
document.write( "- how many liked only one of three foods?<BR>\n" );
document.write( "- how many liked eggs and mackerel but not ham?<BR>\n" );
document.write( "- how many people were surveyed?\r<BR>\n" );
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document.write( "I'm trying to read up on this more, but as my username suggests, I'm still new and having a bit of a hard time. Thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705876 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "According to a survey, 16 people liked ham, 19 liked eggs, 18 liked mackerel, <BR>\n" );
document.write( "8 liked mackerel and eggs, <BR>\n" );
document.write( "5 liked ham and eggs, <BR>\n" );
document.write( "7 liked ham and mackerel, <BR>\n" );
document.write( "and 3 liked all three foods. \r<BR>\n" );
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document.write( "1)  how many liked only mackerel?                     18 - 8 - 7 + 3.\r\n" );
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document.write( "2)  how many liked at least two of three foods?        8 + 5 + 7 - 2*3.\r\n" );
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document.write( "3)  how many liked only one of three foods?           16 + 19 + 18 - 8 - 5 - 7 + 2*3.\r\n" );
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document.write( "4)  how many liked eggs and mackerel but not ham?     19 + 18 - 8 + 3.\r\n" );
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document.write( "5)  how many people were surveyed?                    16 + 19 + 18 - 8 - 5 - 7 + 3.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "First, &nbsp;I put the numbers only in hope that they will explain everything to you without my words.\r<BR>\n" );
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document.write( "But then I put some minimal explanations to worm your mind.\r<BR>\n" );
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document.write( "1) &nbsp;how many liked only mackerel ?                     \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Take those who like mackerel; &nbsp;subtract those who like ME; &nbsp;subtract those who like MH; &nbsp;add MHE what were subtracted twice.\r<BR>\n" );
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document.write( "2) &nbsp;how many liked at least two of three foods ?        <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ME + HE + HM - 2*HEM = 8 + 5 + 7 - 2*3. \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(when we add ME + HE + HM, we count the triple intersection thrice; therefore, I subtract HEM twice . . . )\r<BR>\n" );
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document.write( "The same or similar logic works in other cases . . . \r<BR>\n" );
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document.write( "--------------<BR>\n" );
document.write( "To get familiar with the subject, &nbsp;look into my lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/misc/Advanced-probs-counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Advanced problems on counting elements in sub-sets of a given finite set</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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