Algebraic Properties
Binary union is an associative operation; that is,
- A ∪ (B ∪ C) = (A ∪ B) ∪ C.
The operations can be performed in any order, and the parentheses may be omitted without ambiguity (i.e., either of the above can be expressed equivalently as A ∪ B ∪ C). Similarly, union is commutative, so the sets can be written in any order.
The empty set is an identity element for the operation of union. That is, A ∪ ∅ = A, for any set A.
These facts follow from analogous facts about logical disjunction.
Read more about this topic: Union (set Theory)
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