---
tag: YJEY2EBVJF
kind: statement
role: proposition
name: Principle of duality
aliases: [duality-principle-for-sets]
sources:
  - wikipedia: en:961805@r1367291561
    locator: Algebra of sets, section Principle of duality
    note: adopted
    mention: wikipedia://en/961805#CJLJ
    sections: [Statement]
inventory: [VCE3AWP75G]
---

## Statement

Each of the identities stated above is one of a pair of identities such that each can be transformed into the other by interchanging $\cup$ and $\cap$, while also interchanging $\varnothing$ and $\boldsymbol{U}$.

These are examples of an extremely important and powerful property of set algebra, namely, the **principle of duality** for sets, which asserts that for any true statement about sets, the **dual** statement obtained by interchanging unions and intersections, interchanging $\boldsymbol{U}$ and $\varnothing$ and reversing inclusions is also true. A statement is said to be **self-dual** if it is equal to its own dual.