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Set Unions
Needed by:
Intersection of Empty Set
Set Dualities
Set Unions and Intersections
Successor Sets
Uncertain Outcomes
Unordered Triples
Venn Diagrams
Sheet PDF
Graph PDF

Pair Unions


We often unite the elements of one set with another.


Let $A$ and $B$ denote sets. We call $\cup \set{A, B}$ the pair union of $A$ and $B$. We denote the union of the pair $\set{A, B}$ by $A \cup B$. Clearly the pair union does not depend on the order of $A$ and $B$. In other words, $A \cup B = B \cup A$.


Here are some basic facts about unions of a pair of sets.1 Let $A$ and $B$ denote sets.

$A \cup \varnothing = A$
$A \cup B = B \cup A$
$(A \cup B) \cup C = A \cup (B \cup C)$
$A \cup A = A$.
$A \subset B \iff A \cup B = B$

  1. Proofs will appear in the next edition. ↩︎
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