Empty Intersection iff Subset of Complement/Proof 1
Jump to navigation
Jump to search
Corollary to Intersection with Complement is Empty iff Subset
- $S \cap T = \O \iff S \subseteq \relcomp {} T$
Proof
| \(\ds S \cap T\) | \(=\) | \(\ds \O\) | ||||||||||||
| \(\ds \leadstoandfrom \ \ \) | \(\ds S \cap \relcomp {} {\relcomp {} T}\) | \(=\) | \(\ds \O\) | Complement of Complement | ||||||||||
| \(\ds \leadstoandfrom \ \ \) | \(\ds S\) | \(\subseteq\) | \(\ds \relcomp {} T\) | Intersection with Complement is Empty iff Subset |
$\blacksquare$