document.write( "Question 705548: I am having problems understanding how to show the answer to this problem. If
\n" ); document.write( "If n(A)= 15, n(A n B)=5, and n(A u B)=30, then what is n(B)? I know the answer is 20, I just am not sure of how I got the result. Can you help me? \n" ); document.write( "
Algebra.Com's Answer #434632 by jerryguo41(197)\"\" \"About 
You can put this solution on YOUR website!
n(A) is the population of \"A\"'s
\n" ); document.write( "That includes:
\n" ); document.write( "- n(A n 'B) (A and not B)
\n" ); document.write( "- n(A n B) (Both A and B)\r
\n" ); document.write( "\n" ); document.write( "So, if n(A n B)=5 and n(A)=15:
\n" ); document.write( "n(A n 'B)= 10\r
\n" ); document.write( "\n" ); document.write( "Thus is n(A u B)=30 and n(A n 'B)=10:
\n" ); document.write( "n(B)= 20
\n" ); document.write( "-------------------------------------
\n" ); document.write( "Think of this as a venn diagram\r
\n" ); document.write( "\n" ); document.write( "The left two sections would be called n(A)= 15
\n" ); document.write( "The middle section would be n(A n B)=5
\n" ); document.write( "Thus the left section would be n(A n 'B) = 10
\n" ); document.write( "Finally of both the far left and the far right sections n(A u B)=30;
\n" ); document.write( "n(A u B) - n(A n 'B) = n(B)
\n" ); document.write( "30 - 10 = 20
\n" ); document.write( " \n" ); document.write( "
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