document.write( "Question 1055373: If n(A)=13, n(A∪B)=19, and n(B)=15, what is n(A∩B)? ​\r
\n" ); document.write( "\n" ); document.write( "Please help.
\n" ); document.write( "

Algebra.Com's Answer #670589 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "If n(A)=13, n(A∪B)=19, and n(B)=15, what is n(A∩B)? ​\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "Given n(A)=13.  So n(A) = p+q = 13   \r\n" );
document.write( "\r\n" );
document.write( "Given n(A∪B)=19.  So n(A∪B) = p+q+r = 19 \r\n" );
document.write( "\r\n" );
document.write( "Given n(B)=15. So n(B) = q+r = 15\r\n" );
document.write( "\r\n" );
document.write( "what is n(A∩B).  So that asks: What is q?\r\n" );
document.write( "\r\n" );
document.write( "We have the system of equations:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Subtract the 1st equation from the 2nd and get r=6\r\n" );
document.write( "Subtract the 3rd equation from the 2nd and get p=4\r\n" );
document.write( "Substitute p=4 in the first equation and get q=9\r\n" );
document.write( "\r\n" );
document.write( "So the Venn diagram is like this\r\n" );
document.write( "\r\n" );
document.write( "    \r\n" );
document.write( "\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "You can also do it by memorizing a formula.\r\n" );
document.write( "\r\n" );
document.write( "n(A)=13, n(A∪B)=19, and n(B)=15, what is n(A∩B)\r\n" );
document.write( "\r\n" );
document.write( "n(A∪B) = n(A) + n(B) - n(A∩B)\r\n" );
document.write( "   19  =  13  +  15  -   q\r\n" );
document.write( "\r\n" );
document.write( "   19  =  28 - q\r\n" );
document.write( "\r\n" );
document.write( "    q  =  9\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );