## 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.

For example

has dual

has dual

has dual statement

has dual

Notice here that the complement ofdoes not becomebut stays

Set-theoretic union and intersection are dual under the set complement operator C. That is,

Proof:

More generally,