document.write( "Question 1140918: Hello, my question is about proving a set identity: \r
\n" ); document.write( "\n" ); document.write( "Prove (B - A) U ( C-A ) = ( B U C) - A. \r
\n" ); document.write( "\n" ); document.write( "I know that I must show (B - A) U ( C-A ) is a subset of ( B U C) - A and ( B U C) - A is a subset of (B - A) U ( C-A ), but I am confused on how I should do this.
\n" ); document.write( "I would appreciate some help please. \n" ); document.write( "

Algebra.Com's Answer #761587 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given problem is to prove $\"%28B-A%29U%28C-A%29=%28BUC%29-A\"$ ,\r
\n" ); document.write( "\n" ); document.write( " Let $\"x\"$ be ∈ $\"%28B+-+A%29+U+%28C+-+A%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " => $\"x\"$ ∈ $\"%28B+-+A%29\"$ or $\"x\"$ ∈ $\"%28C+-+A%29\"$ \r
\n" ); document.write( "\n" ); document.write( " = ( $\"x\"$ ∈ $\"B\"$ and $\"x\"$ ∉ $\"A\"$ ) or ( $\"x\"$ ∈ $\"C\"$ and $\"x\"$ ∉ $\"A\"$ )\r
\n" ); document.write( "\n" ); document.write( " = ( $\"x\"$ ∈ $\"B\"$ or $\"x\"$ ∈ $\"C\"$ ) and ( $\"x\"$ ∉ $\"A\"$ )\r
\n" ); document.write( "\n" ); document.write( " = ( $\"x\"$ ∈ $\"B+U+C+\"$ ) and ( $\"x\"$ ∉ $\"A\"$ )\r
\n" ); document.write( "\n" ); document.write( " = $\"x\"$ ∈ $\"%28B+U+C%29+-+A\"$ \r
\n" ); document.write( "\n" ); document.write( "Hence proved $\"%28B+-+A%29+U+%28C+-+A%29+=+%28B+U+C%29+-+A\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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