Set Difference as Intersection with Complement

Theorem
Set difference can be expressed as the intersection with the set complement:


 * $$A \setminus B = A \cap \complement \left({B}\right)$$

Proof
This follows directly from Set Difference Relative Complement:
 * $$A \setminus B = A \cap \complement_S \left({B}\right)$$.

Let $$S = \mathbb{U}$$.

Since $$A, B \in \mathbb{U}$$ by the definition of the universe, the result follows.