# Under what conditions does A\(A\B)=B?

• Sep 19th 2009, 11:28 AM
zhupolongjoe
Under what conditions does A\(A\B)=B?
This was a textbook problem I saw.
It's been hurting my brain a bit...isn't this always going to be true?
• Sep 19th 2009, 11:35 AM
Plato
Quote:

Originally Posted by zhupolongjoe
This was a textbook problem I saw.
It's been hurting my brain a bit...isn't this always going to be true?

$\begin{array}{rcl}
{A\backslash \left( {A\backslash B} \right)} & = & {A \cap \left[ {A \cap B^c } \right]^c } \\
{} & = & {A \cap \left[ {A^c \cup B} \right]} \\
{} & = & {A \cap B} \\ \end{array}$

Now you finish it off.