Intersection with Complement

Theorem
The intersection of a set and its complement is the empty set.

$$S \cap \mathcal{C} \left({S}\right) = \varnothing$$

Proof
Substitute $$\mathbb{U}$$ for $$S$$ and $$S$$ for $$T$$ in $$T \cap \mathcal{C}_S \left({T}\right) = \varnothing$$ from Intersection with Relative Complement.