document.write( "Question 470949: Illustrate a Venn Diagram using this information to fill in the number of elements for each region. n(A union B) = 17, n(A intersect B) = 3, n(A) = 8, (A' union B') = 21. \n" ); document.write( "

Algebra.Com's Answer #323035 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Illustrate a Venn Diagram using this information to fill in the number of elements for each region. n(A union B) = 17, n(A intersect B) = 3, n(A) = 8, (A' union B') = 21.\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "First draw a big rectangle for the universal set:\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Next draw a circle to and label it E:\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Next draw a circle overlapping the first circle and\r\n" );
document.write( "label it B. \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "The overlapping part is the set \"A ᑎ B\".\r\n" );
document.write( "We are given n(A ᑎ B) = 3 , so we write \"3\" in the \r\n" );
document.write( "region that's shaped like this \"()\", the overlapping \r\n" );
document.write( "part opf the two circles: \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Now since n(A) = 8, and the number of elements in\r\n" );
document.write( "the overlapping part, shaped like thisa \"()\"\r\n" );
document.write( "is 3, the probability of being in the rest of circle\r\n" );
document.write( "A is 8 - 3 or 5, so we write 5 in the left part\r\n" );
document.write( "of circle A, so that the total number of elements of \r\n" );
document.write( "in the two parts of circle A is 8.\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "We are given that\r\n" );
document.write( "\r\n" );
document.write( "n(A U B) = 17\r\n" );
document.write( "\r\n" );
document.write( "The union consists of all elements in the circles.\r\n" );
document.write( "We already have the number of elements in 2 of the\r\n" );
document.write( "three regions so there must be 9 in the right part\r\n" );
document.write( "of circle B so that there will be 17 inside the\r\n" );
document.write( "circles.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Any remaining elements are located outside the two\r\n" );
document.write( "circles, yet inside the rectangle.\r\n" );
document.write( "\r\n" );
document.write( "We are given that n(A' U B') = 21\r\n" );
document.write( " \r\n" );
document.write( "By DeMorgan's law, A' U B' = (A ᑎ B)'\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This means that all the elements in all the regions other\r\n" );
document.write( "that the 3 in the intersection must total 21. \r\n" );
document.write( "\r\n" );
document.write( "Other than the 3, we have so far 5 and 9 or 14 elements besides\r\n" );
document.write( "the 3 in the intersection so there must be 21-14 or 7 elements \r\n" );
document.write( "outside the two circles.  So the final Venn diagram is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );