Class Difference of B with Class Difference of A with B/Mistake
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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 $5.6. \ \text {(d)}$
- $\S 5$ The union axiom
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 $5.6. \ \text {(d)}$