Algebra.Com's Answer #740099 by Edwin McCravy(20055)![\"\"](\"/images/stars/stars-13.gif\")  
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if n(A)=80,n(B)=30,n(A U B)=100 then find n [(A-B) U (B-A)]\r\n" );
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document.write( "n(A) = x+y\r\n" );
document.write( "n(B) = y+z\r\n" );
document.write( "n(A-B) = (x+y)-y = x, \r\n" );
document.write( "n(B-A) = (y+z)-y = z,\r\n" );
document.write( "n[(A-B) U (B-A)] = x+z since (A-B) and (B-A) are disjoint\r\n" );
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document.write( "n(A) = x+y = 80\r\n" );
document.write( "n(B) = y+z = 30\r\n" );
document.write( "n(A U B) = x+y+z = 100 \r\n" );
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document.write( "So we have the system of three equations in three unknowns:\r\n" );
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document.write( "x + y = 80\r\n" );
document.write( " y + z = 30\r\n" );
document.write( "x + y + z = 100\r\n" );
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document.write( "Subtracting the first equation from the third gives z = 20\r\n" );
document.write( "Substituting that in the second equation gives y = 10\r\n" );
document.write( "Substituting that in the first equation gives x = 70\r\n" );
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document.write( "Now our Venn diagram becomes\r\n" );
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document.write( "n[(A-B) U (B-A)] = x+z = 70+20 = 90\r\n" );
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document.write( "Edwin \n" );
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