# Duality Principle for Sets

This proof is about Duality Principle in the context of Set Theory. For other uses, see Duality Principle.

## Theorem

Any identity in set theory which uses any or all of the operations:

Set intersection $\cap$
Set union $\cup$
Empty set $\O$
Universal set $\mathbb U$

and none other, remains valid if:

$\cap$ and $\cup$ are exchanged throughout
$\O$ and $\mathbb U$ are exchanged throughout.

## Proof

Follows from:

$\blacksquare$