Set Difference with Set Difference is Union of Set Difference with Intersection/Corollary/Mistake

Source Work

 * Chapter $2$: Some Basics of Class-Set Theory:
 * $\S 5$ The union axiom
 * Exercise $5.6. \ \text {(d)}$
 * Exercise $5.6. \ \text {(d)}$

Mistake

 * ''Show that for any classes $A$, $B$, $\ldots{}$
 * $B - \paren {A - B} = \O$

Correction
From the corollary to Set Difference with Set Difference is Union of Set Difference with Intersection, the correct result is:


 * $B - \paren {A - B} = B$

Perhaps the following exercise might have been meant:


 * ''Show that for any classes $A$, $B$, $\ldots{}$
 * $B \cap \paren {A - B} = \O$

which is proved in Set Difference Intersection with Second Set is Empty Set.