The Principle of Duality
The principle of duality for sets states that for any true statement about sets, the dual statement obtained by interchanging unions and intersections, interchangingandand reversing inclusions is also true. A statement is said to be self-dual if it is equal to its own dual.
has dual statement
Notice here that the complement ofdoes not becomebut stays
Set-theoretic union and intersection are dual under the set complement operator C. That is,