document.write( "Question 1025806: By drawing a Venn diagram, replace the expression with one involving at most one union and the complement symbol applied only to R,S, and T. Simplify the expression. (' is the complement)\r
\n" ); document.write( "\n" ); document.write( " (R∩S)∪(S∩T)∪(R∩S'∩T') \n" ); document.write( "
Algebra.Com's Answer #641284 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(R∩S)∪(S∩T)∪(R∩S'∩T') \r\n" );
document.write( "\r\n" );
document.write( "R∩S is made up of the two regions which are \r\n" );
document.write( "in common to the circles R,S.  They are\r\n" );
document.write( "regions 2&5, So we can substitute 2&5 for R∩S.\r\n" );
document.write( "\r\n" );
document.write( "(2&5)∪(S∩T)∪(R∩S'∩T')\r\n" );
document.write( "\r\n" );
document.write( "S∩T is made up of the two regions which are \r\n" );
document.write( "in common to the circles S,T.  They are\r\n" );
document.write( "regions 5&6, So we can substitute 5&6 for S∩T.\r\n" );
document.write( "\r\n" );
document.write( "(2&5)∪(5&6)∪(R∩S'∩T')\r\n" );
document.write( "\r\n" );
document.write( "R∩S'∩T' is a little more complicated. There are \r\n" );
document.write( "primes (tic marks) on S and T, indicating\r\n" );
document.write( "complements.  That means that R∩S'∩T' is the \r\n" );
document.write( "part of R that is NOT part of S, and also NOT \r\n" );
document.write( "part of T.  That is only the left part of circle \r\n" );
document.write( "R, the one region 1, because it is the only part \r\n" );
document.write( "of R that is NOT part of the other two circles.  \r\n" );
document.write( "So we replace R∩S'∩T' by 1.\r\n" );
document.write( "  \r\n" );
document.write( "(2&5)∪(5&6)∪(1)\r\n" );
document.write( "\r\n" );
document.write( "So we end up with the 4 regions 1&2&5&6, so\r\n" );
document.write( "\r\n" );
document.write( "(R∩S)∪(S∩T)∪(R∩S'∩T') = 1&2&5&6\r\n" );
document.write( "\r\n" );
document.write( "Regions 1 and 2 are the parts of R that are not parts\r\n" );
document.write( "of T. So that's (R∩T')\r\n" );
document.write( "\r\n" );
document.write( "We only need to union that with regions 5 and 6.\r\n" );
document.write( "Regions 5 and 6 are the regions common to S and T\r\n" );
document.write( "\r\n" );
document.write( "(R∩T')∪(S∩T)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );