Exercise 3.1.9: Insufficient Justification for Final Two Steps

[hansonchar]

The existing note includes the following logical steps:

$\iff (x\in A)\wedge (x\not\in B)$ $\iff (x\in A)\qquad\qquad\qquad\qquad (A\cap B=\emptyset).$

However, it’s unclear how the conclusion

$$(x\in A)\wedge (x\not\in B) \iff (x\in A)$$

follows directly from the assumption that

$$A\cap B=\emptyset$$

This seems to require additional justification.