Intersection with Complement

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


 * $$S \cap \complement \left({S}\right) = \varnothing$$

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

Also see

 * Union with Complement