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Union

From AoPSWiki

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.

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