## Union

The union of two sets and is the set obtained by combining the members of each. This is written , and is pronounced  union '' or  cup .'' The union of sets through is written .

Let , , , ... be sets, and let denote the probability of . Then

 (1)

Similarly,
 (2)
If and are Disjoint, by definition , so
 (3)

Continuing, for a set of disjoint elements , , ...,
 (4)

which is the Countable Additivity Probability Axiom. Now let
 (5)

then
 (6)