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

**zhupolongjoe** · September 19th 2009, 10:28 AM

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

**Plato** · September 19th 2009, 10:35 AM

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?

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

Now you finish it off.

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