document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089563>Question 1089563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (A union B)=(A union C) & (A intersection B)=(A intersection C) then PROVE THAT B=C<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704212 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "(A U B) =(A U C)  \r<BR>\n" );
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document.write( "(A &#8745; B)=(A &#8745; C)\r<BR>\n" );
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document.write( "proof:<BR>\n" );
document.write( "(A U B) =(A U C) <BR>\n" );
document.write( "=>(A U B)&#8745; C =(A U C) &#8745; C<BR>\n" );
document.write( "=>(A &#8745; C) U (B&#8745; C) =  C.........(distributive law)<BR>\n" );
document.write( "=>(A  U B) = A U C\r<BR>\n" );
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document.write( "=>(A  U B)&#8745; B  = (A U C) &#8745; B<BR>\n" );
document.write( "=>B  = (A&#8745; B) U (C&#8745; B).........(distributive law)<BR>\n" );
document.write( "=>B  = (A&#8745; C) U (C&#8745; B)................[given (A&#8745; B)=(A&#8745; C) ]<BR>\n" );
document.write( "=>B  = C </SPAN>\n" );
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