document.write( "Question 1206134: Prove 𝐶−𝐷=𝐶∩𝐷'. Just having a little bit of trouble with my wording of the proof. Thank you. \n" ); document.write( "

Algebra.Com's Answer #843379 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Let x be an element of the set  𝐶−𝐷.\r\n" );
document.write( "\r\n" );
document.write( "It means that x does belong to C and does not belong to D.\r\n" );
document.write( "\r\n" );
document.write( "In other words, x does belong to C and does belong to D'.\r\n" );
document.write( "\r\n" );
document.write( "Hence, x belongs to the intersection  𝐶∩𝐷'.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   +----------------------------------------------+\r\n" );
document.write( "   |           Thus we proved that                |\r\n" );
document.write( "   |  the set C-D  is the subset of the set 𝐶∩𝐷'. |\r\n" );
document.write( "   +--------------------------------------------- +\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In opposite, if x is an element of the set 𝐶∩𝐷',\r\n" );
document.write( "then x does belong to C and does belong to D'.\r\n" );
document.write( "\r\n" );
document.write( "It means that x does belong to C and does not belong to D.\r\n" );
document.write( "\r\n" );
document.write( "In other words, x does belong to the set C-D.\r\n" );
document.write( "\r\n" );
document.write( "Hence, x belongs to  𝐶∩𝐷'.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   +-----------------------------------------------+\r\n" );
document.write( "   |           Thus we proved that                 |\r\n" );
document.write( "   |  the set 𝐶∩𝐷'  is the subset of the set C-D.  |\r\n" );
document.write( "   +-----------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies that  C-D = 𝐶∩𝐷'.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "At this point, the proof is complete.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );