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,