Duality Principle for Sets
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This proof is about Duality Principle in the context of Set Theory. For other uses, see Duality Principle.
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.
- 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 5$: Complements and Powers
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.5$. The algebra of sets