Union

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The union of several sets is the set which contains all the elements of each of the given sets. The union of sets $A$ and $B$ is denoted $A\cup B$.

For example, $\{1, 2, 3\} \cup \{0\} = \{0, 1, 2, 3\}$ and $\{1, 2\} \cup \{0, 1\} = \{0, 1, 2\}$ and $\{1, 3, 5, \ldots\} \cup \{0, 2, 4, \ldots\} = \{0, 1, 2, 3, \ldots\}$.

For any sets $A$ and $B$, $A \subseteq A\cup B$ and $B \subseteq A \cup B$. It follows that $A\cup B = A$ if and only if $B \subseteq A$.

See also

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