Duality Principle for Sets

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This proof is about the Duality Principle for Sets. 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 $\varnothing$
Universal set $\mathbb U$

and none other, remains valid if:

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


Proof

Follows from:

$\blacksquare$


Sources