Class Difference of B with Class Difference of A with B/Mistake

Source Work

2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.):

Chapter $2$: Some Basics of Class-Set Theory:

$\S 5$ The union axiom

Exercise $5.6. \ \text {(d)}$

Mistake

Show that for any classes $A$, $B$, $\ldots{}$

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

Correction

From Class Difference of B with Class Difference of A with B, the correct result is:

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

Perhaps the following exercise might have been meant:

Show that for any classes $A$, $B$, $\ldots{}$

$B \cap \paren {A - B} = \O$

the set-theoretical version of which is proved in Set Difference Intersection with Second Set is Empty Set.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 5$ The union axiom: Exercise $5.6. \ \text {(d)}$