document.write( "Question 768220: If Set A has 9 letters and 3 numbers. Set B has 12 letters and 1 number. 9 letters and 1 number is common to both sets. What is the number of elements in set A or set B?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #468628 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Draw two overlapping circles, label one A and one B, like this\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "First look at these words:\r\n" );
document.write( "

\n" ); document.write( "9 letters and 1 number is common to both sets.
\n" ); document.write( "
\r\n" );
document.write( "Letting L stand for a letter and N stand for a number,\r\n" );
document.write( "put 9 L's and 1 N in the part in the middle which is \r\n" );
document.write( "common to both circles, like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next look at these words:\r\n" );
document.write( "

\n" ); document.write( "Set A has 9 letters and 3 numbers.
\n" ); document.write( "
\r\n" );
document.write( "Set A already has 9 letters and 1 number because they are in the part\r\n" );
document.write( "that is in common to both circles.  So set A needs 2 more numbers so\r\n" );
document.write( "it will have 3 numbers.  (It doesn't need any more letters).  So we\r\n" );
document.write( "put 2 N's in the left part of A, like this:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "and now set A has 9 letters and 3 numbers.\r\n" );
document.write( "\r\n" );
document.write( "Next we look at these words:\r\n" );
document.write( "

\n" ); document.write( "Set B has 12 letters and 1 number.
\n" ); document.write( "
\r\n" );
document.write( "Set B already has 9 letters and 1 number because they are in the part\r\n" );
document.write( "that is in common to both circles.  So set B needs 3 more letters so\r\n" );
document.write( "it will have 12 letters.  (It doesn't need any more numbers).  So we\r\n" );
document.write( "put 3 L's in the right part of B, like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and now set B has 12 letters and 1 number.\r\n" );
document.write( "\r\n" );
document.write( "Now the question is:\r\n" );
document.write( "

\n" ); document.write( "What is the number of elements in set A or set B?
\n" ); document.write( "
\r\n" );
document.write( "If we count all the L's and N's that are in either one of the\r\n" );
document.write( "two sets, we see there are 12 L's and 3 N's, so that makes 15\r\n" );
document.write( "elements.\r\n" );
document.write( "\r\n" );
document.write( "Answer: 15 elements.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );