\r\n" );
document.write( "None of those turn out to have the same Venn diagram.\r\n" );
document.write( "I'll go through them to show what regions are to be shaded in each:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "The sets are denoted by capital letters A,B, C\r\n" );
document.write( "\r\n" );
document.write( "The disjoint regions that make them up are denoted with small letters.\r\n" );
document.write( "\r\n" );
document.write( "Since I can't shade anything on here, I will use the convenient although \r\n" );
document.write( "non-standard notation that when small letters are written side by side it \r\n" );
document.write( "means the union of those regions.\r\n" );
document.write( "\r\n" );
document.write( "So A = degh, B= efhi, C= ghij\r\n" );
document.write( "\r\n" );
document.write( "A' ∪ (B ∩ C)\r\n" );
document.write( "\r\n" );
document.write( "degh' ∪ (efhi ∩ ghij)\r\n" );
document.write( "\r\n" );
document.write( "Do the parentheses first. ∩ means to take only the regions in common,\r\n" );
document.write( "so the parentheses becomes hi\r\n" );
document.write( "\r\n" );
document.write( "degh' ∪ hi\r\n" );
document.write( "\r\n" );
document.write( "degh' means to take all the regions in the entire Venn diagram \r\n" );
document.write( "EXCEPT degh, which means fijk, so the above becomes:\r\n" );
document.write( "\r\n" );
document.write( "fijk ∪ hi\r\n" );
document.write( "\r\n" );
document.write( "The ∪ means to take all the regions that are on either side of the ∪ \r\n" );
document.write( "\r\n" );
document.write( "So the answer is this union of regions:\r\n" );
document.write( "\r\n" );
document.write( "fhijk\r\n" );
document.write( "\r\n" );
document.write( "So you would draw a Venn diagram and shade regions f,i,j,k,g, and h\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------------\r\n" );
document.write( "A ∩ (B' ∪ C')\r\n" );
document.write( "\r\n" );
document.write( "degh ∩ (efhi' ∪ ghij')\r\n" );
document.write( "\r\n" );
document.write( "efhi' means to take all the regions in the entire Venn diagram \r\n" );
document.write( "EXCEPT efhi, which means dgjk, so the above becomes:\r\n" );
document.write( "\r\n" );
document.write( "degh ∩ (dgjk ∪ ghij')\r\n" );
document.write( "\r\n" );
document.write( "ghij' means to take all the regions in the entire Venn diagram \r\n" );
document.write( "EXCEPT ghij, which means defk, so the above becomes:\r\n" );
document.write( "\r\n" );
document.write( "degh ∩ (dgjk ∪ defk)\r\n" );
document.write( "\r\n" );
document.write( "The ∪ means to take all the regions that are on either side of the ∪,\r\n" );
document.write( "so the parentheses becomes defgjk, and we have:\r\n" );
document.write( "\r\n" );
document.write( "degh ∩ defgjk\r\n" );
document.write( "\r\n" );
document.write( "∩ means to take only the regions in common, so we get this:\r\n" );
document.write( "\r\n" );
document.write( "deg\r\n" );
document.write( "\r\n" );
document.write( "So you would draw a Venn diagram and shade regions d,e, and g\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------\r\n" );
document.write( "\r\n" );
document.write( "A ∩ B ∩ C\r\n" );
document.write( "\r\n" );
document.write( "degh ∩ efhi ∩ ghij\r\n" );
document.write( "\r\n" );
document.write( "Since ∩ means to take only the regions in common, h is the only\r\n" );
document.write( "region in common, so this becomes only \r\n" );
document.write( "\r\n" );
document.write( "h\r\n" );
document.write( "So you would draw a Venn diagram and shade only the middle region h\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "\r\n" );
document.write( "A ∩ B' ∩ C'\r\n" );
document.write( "\r\n" );
document.write( "degh ∩ efhi' ∩ ghij'\r\n" );
document.write( "\r\n" );
document.write( "The apostrophes are \"complements\" which means to take all the regions \r\n" );
document.write( "in the entire Venn diagram EXCEPT the ones before the ', so the above\r\n" );
document.write( "becomes:\r\n" );
document.write( "\r\n" );
document.write( "degh ∩ dgjk ∩ defk\r\n" );
document.write( "\r\n" );
document.write( "∩ means to take only the regions in common, so that becomes only d\r\n" );
document.write( "\r\n" );
document.write( "d\r\n" );
document.write( "\r\n" );
document.write( "So you would draw a Venn diagram and shade only the upper left region d\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
