### Chapter 3. Probability: Relationships between Events

### Union

When considering two events #A# and #B#, it could be of interest to investigate the scenario of #A# OR #B# happening. That means that either one of the following things happens:

- #A# happens and #B# does not happen
- #B# happens and #A# does not happen
- #A# and #B# both happen

The combined event of #A# OR #B# happening is called the *union* of #A# and #B#.

Union

**Definition**

The **union** of two events #A# and #B# is the set of outcomes that are classified as #A# OR #B#.

The union of events #A# and #B# is denoted as #A \cup B#.

All of #A# is contained in #A \cup B# and all of #B# is contained in #A \cup B#. Additionally, the outcomes that are in both #A# and #B# are contained in #A \cup B#.

Outcomes that are classified as #A# and #B# should only be listed once; every outcome is unique.

The union of #A# and #B# is the set of outcomes that are classified as either #A# OR #B#:

\[A \cup B = \{1, 2, 3, 4, 5, 6\}\]

\[A \cup B = \{1, 2, 3, 4, 5, 6\}\]

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